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  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.


Results (12 matches)

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Label Base field Conductor Isogeny class Weierstrass coefficients
20.2-a1 4.4.12400.1 20.2 20.2-a \( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{9}{2} a + \frac{9}{2}\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a\) , \( \frac{25}{2} a^{3} - 31 a^{2} - \frac{213}{2} a + 227\) , \( 100 a^{3} - \frac{385}{2} a^{2} - 824 a + \frac{3181}{2}\bigr] \)
20.2-a2 4.4.12400.1 20.2 20.2-a \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - \frac{5}{2}\) , \( -\frac{1}{2} a^{2} + a + \frac{9}{2}\) , \( 1\) , \( -\frac{535}{2} a^{3} - \frac{1509}{2} a^{2} + \frac{2047}{2} a + \frac{5661}{2}\) , \( 7835 a^{3} + \frac{44931}{2} a^{2} - 29505 a - \frac{169025}{2}\bigr] \)
20.2-a3 4.4.12400.1 20.2 20.2-a \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - \frac{5}{2}\) , \( -\frac{1}{2} a^{2} + a + \frac{9}{2}\) , \( 1\) , \( -\frac{615}{2} a^{3} - \frac{1389}{2} a^{2} + \frac{2667}{2} a + \frac{4561}{2}\) , \( 7893 a^{3} + \frac{41839}{2} a^{2} - 31319 a - \frac{151229}{2}\bigr] \)
20.2-a4 4.4.12400.1 20.2 20.2-a \( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a\) , \( \frac{1}{2} a^{2} + a - \frac{7}{2}\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{7}{2}\) , \( -\frac{883}{2} a^{3} + \frac{1699}{2} a^{2} + \frac{7273}{2} a - \frac{14081}{2}\) , \( \frac{21077}{2} a^{3} - 20505 a^{2} - \frac{173719}{2} a + 168747\bigr] \)
20.2-b1 4.4.12400.1 20.2 20.2-b \( \bigl[a\) , \( \frac{1}{2} a^{3} - \frac{9}{2} a - 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{5}{2}\) , \( -\frac{1}{2} a^{3} - 4 a^{2} + \frac{5}{2} a + 24\) , \( -\frac{3}{2} a^{2} - 2 a + \frac{9}{2}\bigr] \)
20.2-b2 4.4.12400.1 20.2 20.2-b \( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a + \frac{5}{2}\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a + 1\) , \( \frac{31}{2} a^{3} + \frac{87}{2} a^{2} - \frac{117}{2} a - \frac{327}{2}\) , \( -22 a^{3} - 64 a^{2} + 83 a + 241\bigr] \)
20.2-c1 4.4.12400.1 20.2 20.2-c \( \bigl[\frac{1}{2} a^{2} - \frac{5}{2}\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - \frac{5}{2}\) , \( \frac{3}{2} a^{2} - \frac{15}{2}\) , \( \frac{1}{2} a^{2} - \frac{11}{2}\bigr] \)
20.2-c2 4.4.12400.1 20.2 20.2-c \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{7}{2}\) , \( a\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a + 1\) , \( \frac{13}{2} a^{3} + 18 a^{2} - \frac{49}{2} a - 66\) , \( a^{3} + 4 a^{2} - 3 a - 18\bigr] \)
20.2-d1 4.4.12400.1 20.2 20.2-d \( \bigl[1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{5}{2}\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a + 1\) , \( \frac{59}{2} a^{3} - 58 a^{2} - \frac{485}{2} a + 475\) , \( -\frac{491}{2} a^{3} + 473 a^{2} + \frac{4033}{2} a - 3901\bigr] \)
20.2-d2 4.4.12400.1 20.2 20.2-d \( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{7}{2} a + \frac{7}{2}\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a + 1\) , \( -106 a^{3} - 280 a^{2} + 421 a + 1009\) , \( 1829 a^{3} + \frac{10915}{2} a^{2} - 6690 a - \frac{41841}{2}\bigr] \)
20.2-d3 4.4.12400.1 20.2 20.2-d \( \bigl[\frac{1}{2} a^{2} + a - \frac{5}{2}\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a + \frac{5}{2}\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a + 1\) , \( -717 a^{3} - \frac{3973}{2} a^{2} + 2762 a + \frac{14697}{2}\) , \( 32235 a^{3} + 93032 a^{2} - 120844 a - 351115\bigr] \)
20.2-d4 4.4.12400.1 20.2 20.2-d \( \bigl[1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{5}{2}\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a + 1\) , \( -\frac{341}{2} a^{3} + 302 a^{2} + \frac{2795}{2} a - 2605\) , \( -\frac{4971}{2} a^{3} + 4649 a^{2} + \frac{40417}{2} a - 38557\bigr] \)
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