Elliptic curves over \(\Q(\sqrt{5}, \sqrt{7})\) of conductor 25.1

Base field	Conductor norm	Rank*	Torsion order	CM discriminant
Base field degree	Base change curves	\(\Q\)-curves	Torsion structure	CM
Analytic order* of Ш	Cyclic isogeny degree	Isogeny class size	Semistable	j-invariant
Regulator*	Curves per isogeny class	Isogeny class degree	Potential good reduction

  *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 (6 matches)

 

Label	Base field	Conductor	Isogeny class	Weierstrass coefficients
25.1-a1	\(\Q(\sqrt{5}, \sqrt{7})\)	25.1	25.1-a	\( \bigl[0\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( \frac{11}{23} a^{3} - \frac{5}{23} a^{2} - \frac{156}{23} a + \frac{6}{23}\) , \( -\frac{11}{23} a^{3} + \frac{5}{23} a^{2} + \frac{179}{23} a + \frac{40}{23}\bigr] \)
25.1-b1	\(\Q(\sqrt{5}, \sqrt{7})\)	25.1	25.1-b	\( \bigl[0\) , \( 0\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( -12 a^{2} + 12 a + 25\) , \( -\frac{582}{23} a^{3} + \frac{873}{23} a^{2} + \frac{967}{23} a - \frac{698}{23}\bigr] \)
25.1-c1	\(\Q(\sqrt{5}, \sqrt{7})\)	25.1	25.1-c	\( \bigl[0\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( -\frac{5}{23} a^{3} - \frac{4}{23} a^{2} + \frac{27}{23} a + \frac{106}{23}\) , \( -\frac{3}{23} a^{3} - \frac{7}{23} a^{2} + \frac{7}{23} a - \frac{79}{23}\bigr] \)
25.1-d1	\(\Q(\sqrt{5}, \sqrt{7})\)	25.1	25.1-d	\( \bigl[0\) , \( 0\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a - \frac{22}{23}\) , \( \frac{96}{23} a^{3} - \frac{144}{23} a^{2} - \frac{2064}{23} a - \frac{1865}{23}\) , \( -44 a^{3} + 66 a^{2} + 946 a + 853\bigr] \)
25.1-e1	\(\Q(\sqrt{5}, \sqrt{7})\)	25.1	25.1-e	\( \bigl[0\) , \( \frac{3}{23} a^{3} - \frac{16}{23} a^{2} - \frac{30}{23} a + \frac{102}{23}\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( \frac{11}{23} a^{3} - \frac{5}{23} a^{2} - \frac{156}{23} a + \frac{6}{23}\) , \( \frac{9}{23} a^{3} - \frac{2}{23} a^{2} - \frac{136}{23} a - \frac{200}{23}\bigr] \)
25.1-f1	\(\Q(\sqrt{5}, \sqrt{7})\)	25.1	25.1-f	\( \bigl[0\) , \( \frac{1}{23} a^{3} - \frac{13}{23} a^{2} + \frac{13}{23} a + \frac{103}{23}\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( -\frac{5}{23} a^{3} - \frac{4}{23} a^{2} + \frac{27}{23} a + \frac{106}{23}\) , \( \frac{1}{23} a^{3} + \frac{10}{23} a^{2} + \frac{36}{23} a - \frac{81}{23}\bigr] \)