Elliptic curves over \(\Q(\sqrt{437}) \)

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	$2$	$19$	\(\Q(\sqrt{437}) \)	$2$	$[2, 0]$	1.1	\( 1 \)	\( 1 \)	$1.86801$	$\textsf{none}$	0	$\mathsf{trivial}$	$\textsf{potential}$	$-19$	$N(\mathrm{U}(1))$	✓		✓	✓	$23$	23Ns.2.1	$4$	\( 1 \)	$1$	$17.56070946$	3.360170623	\( -884736 \)	\( \bigl[0\) , \( 0\) , \( 1\) , \( 2 a - 22\) , \( 5 a - 55\bigr] \)	${y}^2+{y}={x}^{3}+\left(2a-22\right){x}+5a-55$
1.1-a2	1.1-a	$2$	$19$	\(\Q(\sqrt{437}) \)	$2$	$[2, 0]$	1.1	\( 1 \)	\( 1 \)	$1.86801$	$\textsf{none}$	0	$\mathsf{trivial}$	$\textsf{potential}$	$-19$	$N(\mathrm{U}(1))$	✓		✓	✓	$23$	23Ns.2.1	$4$	\( 1 \)	$1$	$17.56070946$	3.360170623	\( -884736 \)	\( \bigl[0\) , \( 0\) , \( 1\) , \( -2 a - 20\) , \( -5 a - 50\bigr] \)	${y}^2+{y}={x}^{3}+\left(-2a-20\right){x}-5a-50$
4.1-a1	4.1-a	$1$	$1$	\(\Q(\sqrt{437}) \)	$2$	$[2, 0]$	4.1	\( 2^{2} \)	\( 2^{6} \)	$2.64177$	$(2)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$3$	3Nn	$1$	\( 1 \)	$1$	$19.84955375$	0.949532926	\( -\frac{27}{8} \)	\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 14 a + 290\) , \( 71 a + 1055\bigr] \)	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(14a+290\right){x}+71a+1055$
4.1-b1	4.1-b	$1$	$1$	\(\Q(\sqrt{437}) \)	$2$	$[2, 0]$	4.1	\( 2^{2} \)	\( 2^{6} \)	$2.64177$	$(2)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$3$	3Nn	$1$	\( 1 \)	$1$	$19.84955375$	0.949532926	\( -\frac{27}{8} \)	\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -14 a + 195\) , \( -58 a + 822\bigr] \)	${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-14a+195\right){x}-58a+822$

 

  *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.