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
16.1-a1	16.1-a	$2$	$2$	4.4.9909.1	$4$	$[4, 0]$	16.1	\( 2^{4} \)	\( 2^{4} \)	$12.57965$	$(2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	\( 1 \)	$0.390079341$	$529.1940998$	2.073733912	\( -720868474875 a^{3} + \frac{2726844170253}{2} a^{2} + \frac{3499385683905}{2} a - 1144450579761 \)	\( \bigl[a^{2} - 3\) , \( a^{2} - a - 3\) , \( a^{2} - 3\) , \( 104 a^{3} + 58 a^{2} - 602 a - 641\) , \( -354 a^{3} - 185 a^{2} + 2035 a + 2117\bigr] \)	${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(104a^{3}+58a^{2}-602a-641\right){x}-354a^{3}-185a^{2}+2035a+2117$
16.1-b1	16.1-b	$2$	$2$	4.4.9909.1	$4$	$[4, 0]$	16.1	\( 2^{4} \)	\( 2^{4} \)	$12.57965$	$(2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	\( 1 \)	$1.541049041$	$201.2992047$	3.116331176	\( -720868474875 a^{3} + \frac{2726844170253}{2} a^{2} + \frac{3499385683905}{2} a - 1144450579761 \)	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 16 a^{3} + 8 a^{2} - 86 a - 106\) , \( 12 a^{3} + 2 a^{2} - 55 a - 81\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(16a^{3}+8a^{2}-86a-106\right){x}+12a^{3}+2a^{2}-55a-81$

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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.