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
320.1-g6	320.1-g	$8$	$16$	\(\Q(\zeta_{20})^+\)	$4$	$[4, 0]$	320.1	\( 2^{6} \cdot 5 \)	\( 2^{16} \cdot 5^{4} \)	$8.21859$	$(a), (a^3-a^2-3a+2)$	$0$	$\Z/2\Z\oplus\Z/8\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{4} \)	$1$	$1242.963413$	1.737094179	\( \frac{55296}{5} \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( 1\bigr] \)	${y}^2={x}^{3}-2{x}+1$
320.1-h6	320.1-h	$8$	$16$	\(\Q(\zeta_{20})^+\)	$4$	$[4, 0]$	320.1	\( 2^{6} \cdot 5 \)	\( 2^{16} \cdot 5^{4} \)	$8.21859$	$(a), (a^3-a^2-3a+2)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{3} \)	$0.233348375$	$265.8178999$	2.773984325	\( \frac{55296}{5} \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( -1\bigr] \)	${y}^2={x}^{3}-2{x}-1$

 

  *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.