Elliptic curve search results

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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
52.1-g3	52.1-g	$3$	$9$	\(\Q(\sqrt{65}) \)	$2$	$[2, 0]$	52.1	\( 2^{2} \cdot 13 \)	\( 2^{14} \cdot 13^{2} \)	$1.93462$	$(2,a), (2,a+1), (13,a+6)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3B	$1$	\( 2 \)	$1$	$21.53136195$	5.341273529	\( \frac{12167}{26} \)	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -872 a + 3952\) , \( -48214 a + 218464\bigr] \)	${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-872a+3952\right){x}-48214a+218464$
52.1-j3	52.1-j	$3$	$9$	\(\Q(\sqrt{65}) \)	$2$	$[2, 0]$	52.1	\( 2^{2} \cdot 13 \)	\( 2^{2} \cdot 13^{2} \)	$1.93462$	$(2,a), (2,a+1), (13,a+6)$	$1$	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3B.1.1	$1$	\( 2 \)	$0.886022883$	$21.53136195$	1.051664571	\( \frac{12167}{26} \)	\( \bigl[1\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}$

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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.