Elliptic curves over \(\Q(\sqrt{-3}) \) of conductor 8281.1

Base field	Conductor norm	Rank*	Torsion order	CM discriminant
Base field degree/signature	Bad \(p\)	$\Q$-curves	Torsion structure	CM
Analytic order of Ш*	Cyclic isogeny degree	Isogeny class size	Reduction	Galois image
j-invariant	Regulator*	Curves per isogeny class	Isogeny class degree	Nonmax$\ \ell$

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Results (5 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
8281.1-CMe1	8281.1-CMe	$1$	$1$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	8281.1	\( 7^{2} \cdot 13^{2} \)	\( 7^{10} \cdot 13^{8} \)	$1.47645$	$(-3a+1), (-4a+1)$	$0$	$\mathsf{trivial}$	$\textsf{yes}$	$-3$	$\mathrm{U}(1)$	✓			✓	$7$	7Cs.2.1	$1$	\( 1 \)	$1$	$0.501915664$	0.579562288	\( 0 \)	\( \bigl[0\) , \( a + 1\) , \( a\) , \( a\) , \( -1042 a + 1066\bigr] \)	${y}^2+a{y}={x}^{3}+\left(a+1\right){x}^{2}+a{x}-1042a+1066$
8281.1-CMd1	8281.1-CMd	$1$	$1$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	8281.1	\( 7^{2} \cdot 13^{2} \)	\( 7^{10} \cdot 13^{2} \)	$1.47645$	$(-3a+1), (-4a+1)$	$0$	$\mathsf{trivial}$	$\textsf{yes}$	$-3$	$\mathrm{U}(1)$	✓			✓			$1$	\( 1 \)	$1$	$1.809682664$	2.089641546	\( 0 \)	\( \bigl[0\) , \( -a - 1\) , \( a\) , \( a\) , \( -26 a + 9\bigr] \)	${y}^2+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+a{x}-26a+9$
8281.1-CMc1	8281.1-CMc	$1$	$1$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	8281.1	\( 7^{2} \cdot 13^{2} \)	\( 7^{6} \cdot 13^{10} \)	$1.47645$	$(-3a+1), (-4a+1)$	$0$	$\mathsf{trivial}$	$\textsf{yes}$	$-3$	$\mathrm{U}(1)$	✓			✓	$13$	13Cs.5.1	$1$	\( 1 \)	$1$	$0.626142050$	0.723006563	\( 0 \)	\( \bigl[0\) , \( -a - 1\) , \( a\) , \( a\) , \( -623 a + 376\bigr] \)	${y}^2+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+a{x}-623a+376$
8281.1-CMb1	8281.1-CMb	$1$	$1$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	8281.1	\( 7^{2} \cdot 13^{2} \)	\( 7^{6} \cdot 13^{4} \)	$1.47645$	$(-3a+1), (-4a+1)$	$0$	$\mathsf{trivial}$	$\textsf{yes}$	$-3$	$\mathrm{U}(1)$	✓			✓	$7, 13$	7Cs.2.1, 13Cs.5.1	$1$	\( 1 \)	$1$	$2.257587269$	2.606837235	\( 0 \)	\( \bigl[0\) , \( a + 1\) , \( a\) , \( a\) , \( -11 a - 1\bigr] \)	${y}^2+a{y}={x}^{3}+\left(a+1\right){x}^{2}+a{x}-11a-1$
8281.1-CMa1	8281.1-CMa	$1$	$1$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	8281.1	\( 7^{2} \cdot 13^{2} \)	\( 7^{2} \cdot 13^{6} \)	$1.47645$	$(-3a+1), (-4a+1)$	$0$	$\mathsf{trivial}$	$\textsf{yes}$	$-3$	$\mathrm{U}(1)$	✓			✓	$7$	7Cs.6.1	$1$	\( 1 \)	$1$	$2.816350280$	3.252041185	\( 0 \)	\( \bigl[0\) , \( -a - 1\) , \( a\) , \( a\) , \( -4 a - 3\bigr] \)	${y}^2+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+a{x}-4a-3$

 

  *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.