Elliptic curves over \(\Q(\sqrt{469}) \)

Results (4 matches)

 

Label	Class	Class size	Class degree	Base field	Field degree	Field signature	Conductor	Conductor norm	Discriminant norm	Root analytic conductor	Bad primes	Rank	Torsion	CM	CM	Sato-Tate	$\Q$-curve	Base change	Semistable	Potentially good	Nonmax $\ell$	mod-$\ell$ images	$Ш_{\textrm{an}}$	Tamagawa	Regulator	Period	Leading coeff	j-invariant	Weierstrass coefficients	Weierstrass equation
1.1-a1	1.1-a	$4$	$14$	\(\Q(\sqrt{469}) \)	$2$	$[2, 0]$	1.1	\( 1 \)	\( 1 \)	$1.93520$	$\textsf{none}$	0	$\Z/2\Z$	$\textsf{potential}$	$-7$	$N(\mathrm{U}(1))$	✓		✓	✓	$67$	67Ns.4.1	$1$	\( 1 \)	$1$	$26.16385905$	0.302033689	\( -3375 \)	\( \bigl[1\) , \( -1\) , \( 1\) , \( 3960 a - 44860\) , \( -549848 a + 6228790\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(3960a-44860\right){x}-549848a+6228790$
1.1-a2	1.1-a	$4$	$14$	\(\Q(\sqrt{469}) \)	$2$	$[2, 0]$	1.1	\( 1 \)	\( 1 \)	$1.93520$	$\textsf{none}$	0	$\Z/2\Z$	$\textsf{potential}$	$-7$	$N(\mathrm{U}(1))$	✓		✓	✓	$67$	67Ns.4.1	$1$	\( 1 \)	$1$	$26.16385905$	0.302033689	\( -3375 \)	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 16723092 a - 189442216\) , \( 150738790417 a - 1707599753734\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(16723092a-189442216\right){x}+150738790417a-1707599753734$
1.1-a3	1.1-a	$4$	$14$	\(\Q(\sqrt{469}) \)	$2$	$[2, 0]$	1.1	\( 1 \)	\( 1 \)	$1.93520$	$\textsf{none}$	0	$\Z/2\Z$	$\textsf{potential}$	$-28$	$N(\mathrm{U}(1))$	✓		✓	✓	$67$	67Ns.4.1	$1$	\( 1 \)	$1$	$26.16385905$	0.302033689	\( 16581375 \)	\( \bigl[1\) , \( -1\) , \( 1\) , \( 67320 a - 762615\) , \( -31301736 a + 354592448\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(67320a-762615\right){x}-31301736a+354592448$
1.1-a4	1.1-a	$4$	$14$	\(\Q(\sqrt{469}) \)	$2$	$[2, 0]$	1.1	\( 1 \)	\( 1 \)	$1.93520$	$\textsf{none}$	0	$\Z/2\Z$	$\textsf{potential}$	$-28$	$N(\mathrm{U}(1))$	✓		✓	✓	$67$	67Ns.4.1	$1$	\( 1 \)	$1$	$26.16385905$	0.302033689	\( 16581375 \)	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 284292357 a - 3220521411\) , \( 8587483473480 a - 97280763892594\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(284292357a-3220521411\right){x}+8587483473480a-97280763892594$

 

  *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.