The cuspidal class number formula for the modular curves X1(2p)
Let p be a prime not equal to 2 or 3. We determine the group of all modular units on the modular curve X1(2p), and its full cuspidal class number. We mention a fact concerning the non-existence of torsion points of order 5 or 7 of elliptic curves over Q of square-free conductor n as an application o...
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| Veröffentlicht in: | Journal of the Mathematical Society of Japan 2012-01, Vol.64 (1), p.23-85 |
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| container_title | Journal of the Mathematical Society of Japan |
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| creator | TAKAGI, Toshikazu |
| description | Let p be a prime not equal to 2 or 3. We determine the group of all modular units on the modular curve X1(2p), and its full cuspidal class number. We mention a fact concerning the non-existence of torsion points of order 5 or 7 of elliptic curves over Q of square-free conductor n as an application of a result by Agashe and the cuspidal class number formula for X0(n). We also state the formula for the order of the subgroup of the Q-rational torsion subgroup of J1(2p) generated by the Q-rational cuspidal divisors of degree 0. |
| doi_str_mv | 10.2969/jmsj/06410023 |
| format | Article |
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We determine the group of all modular units on the modular curve X1(2p), and its full cuspidal class number. We mention a fact concerning the non-existence of torsion points of order 5 or 7 of elliptic curves over Q of square-free conductor n as an application of a result by Agashe and the cuspidal class number formula for X0(n). We also state the formula for the order of the subgroup of the Q-rational torsion subgroup of J1(2p) generated by the Q-rational cuspidal divisors of degree 0.</abstract><pub>Mathematical Society of Japan</pub><doi>10.2969/jmsj/06410023</doi><tpages>63</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Journal of the Mathematical Society of Japan, 2012-01, Vol.64 (1), p.23-85 |
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| source | EZB-FREE-00999 freely available EZB journals |
| subjects | 11F03 11G05 11G18 14G05 14G35 14H40 14H52 cuspidal class number elliptic curve Jacobian variety modular curve modular unit torsion subgroup |
| title | The cuspidal class number formula for the modular curves X1(2p) |
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