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
50.3-f1	50.3-f	$2$	$5$	\(\Q(\sqrt{26}) \)	$2$	$[2, 0]$	50.3	\( 2 \cdot 5^{2} \)	\( - 2^{14} \cdot 5^{8} \)	$2.42325$	$(2,a), (5,a+1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$5$	5B	$1$	\( 2 \cdot 3 \)	$0.098495863$	$22.13612461$	2.565571704	\( -\frac{88209}{2} a + \frac{444501}{2} \)	\( \bigl[a\) , \( 1\) , \( 0\) , \( -1633 a - 8308\) , \( 100258 a + 511233\bigr] \)	${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-1633a-8308\right){x}+100258a+511233$
50.3-k1	50.3-k	$2$	$5$	\(\Q(\sqrt{26}) \)	$2$	$[2, 0]$	50.3	\( 2 \cdot 5^{2} \)	\( - 2^{2} \cdot 5^{8} \)	$2.42325$	$(2,a), (5,a+1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$5$	5B	$1$	\( 2 \)	$1$	$22.13612461$	4.341251205	\( -\frac{88209}{2} a + \frac{444501}{2} \)	\( \bigl[1\) , \( -1\) , \( 1\) , \( 13 a - 67\) , \( -61 a + 311\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(13a-67\right){x}-61a+311$

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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.