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
32.2-a2	32.2-a	$2$	$17$	\(\Q(\sqrt{-127}) \)	$2$	$[0, 1]$	32.2	\( 2^{5} \)	\( 2^{30} \cdot 11^{12} \)	$2.39512$	$(2,a), (2,a+1)$	$2$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$17$	17B	$1$	\( 2^{2} \)	$0.514595823$	$2.451929956$	3.582798921	\( -\frac{6357609}{131072} a + \frac{1888137}{4096} \)	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -44 a + 648\) , \( -476 a + 7792\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^3+\left(-a-1\right){x}^2+\left(-44a+648\right){x}-476a+7792$
32.5-a2	32.5-a	$2$	$17$	\(\Q(\sqrt{-127}) \)	$2$	$[0, 1]$	32.5	\( 2^{5} \)	\( 2^{42} \)	$2.39512$	$(2,a), (2,a+1)$	$2$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$17$	17B	$1$	\( 2^{2} \)	$0.514595823$	$2.451929956$	3.582798921	\( -\frac{6357609}{131072} a + \frac{1888137}{4096} \)	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -4\) , \( -2 a + 58\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^3+{x}^2-4{x}-2a+58$

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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.