Elliptic curve search results

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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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
1452.1-h2	1452.1-h	$4$	$6$	\(\Q(\sqrt{21}) \)	$2$	$[2, 0]$	1452.1	\( 2^{2} \cdot 3 \cdot 11^{2} \)	\( 2^{2} \cdot 3^{12} \cdot 11^{4} \)	$2.52778$	$(-a+2), (2), (11)$	$0$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B.1.2	$4$	\( 2^{2} \)	$1$	$2.444595345$	2.133817754	\( \frac{9938375}{176418} \)	\( \bigl[a\) , \( 1\) , \( a + 1\) , \( -23 a + 62\) , \( 463 a - 1295\bigr] \)	${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-23a+62\right){x}+463a-1295$
1452.1-j2	1452.1-j	$4$	$6$	\(\Q(\sqrt{21}) \)	$2$	$[2, 0]$	1452.1	\( 2^{2} \cdot 3 \cdot 11^{2} \)	\( 2^{2} \cdot 3^{12} \cdot 11^{4} \)	$2.52778$	$(-a+2), (2), (11)$	$1$	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B.1.1	$1$	\( 2^{3} \cdot 3 \)	$3.264044740$	$5.718193122$	5.430552431	\( \frac{9938375}{176418} \)	\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( 20\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}+4{x}+20$

 

  *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.