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
605.1-c4	605.1-c	$6$	$8$	\(\Q(\sqrt{5}) \)	$2$	$[2, 0]$	605.1	\( 5 \cdot 11^{2} \)	\( 5^{2} \cdot 11^{8} \)	$0.99097$	$(-2a+1), (-3a+2), (-3a+1)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$1$	\( 2^{3} \)	$0.596122623$	$4.232646692$	1.128398811	\( \frac{2749884201}{73205} \)	\( \bigl[1\) , \( -1\) , \( 0\) , \( -29\) , \( -52\bigr] \)	${y}^2+{x}{y}={x}^{3}-{x}^{2}-29{x}-52$
3025.1-b4	3025.1-b	$6$	$8$	\(\Q(\sqrt{5}) \)	$2$	$[2, 0]$	3025.1	\( 5^{2} \cdot 11^{2} \)	\( 5^{8} \cdot 11^{8} \)	$1.48185$	$(-2a+1), (-3a+2), (-3a+1)$	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	\( 2^{4} \)	$1$	$5.299986074$	2.370225828	\( \frac{2749884201}{73205} \)	\( \bigl[\phi + 1\) , \( 1\) , \( 0\) , \( -145 \phi - 145\) , \( 1040 \phi + 780\bigr] \)	${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-145\phi-145\right){x}+1040\phi+780$

 

  *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.