Elliptic curve search results

Results (unique match)

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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
1089.1-c1	1089.1-c	$4$	$4$	\(\Q(\sqrt{13}) \)	$2$	$[2, 0]$	1089.1	\( 3^{2} \cdot 11^{2} \)	\( 3^{6} \cdot 11^{2} \)	$1.85083$	$(-a), (-a+1), (11)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	\( 2^{3} \)	$1$	$13.37399948$	1.854640035	\( -\frac{180971}{891} a - \frac{75100}{891} \)	\( \bigl[1\) , \( a\) , \( a + 1\) , \( -2 a + 5\) , \( 6 a - 16\bigr] \)	${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-2a+5\right){x}+6a-16$

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  *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.