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
11.1-a1	11.1-a	$6$	$8$	4.4.7625.1	$4$	$[4, 0]$	11.1	\( 11 \)	\( 11 \)	$10.53010$	$(1/4a^3-1/4a^2-9/4a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$4$	\( 1 \)	$1$	$108.5277066$	1.242855680	\( \frac{7273468393095067}{22} a^{3} + \frac{14302897799889049}{22} a^{2} - \frac{2093855705464743}{2} a - \frac{19615292432376359}{11} \)	\( \bigl[a^{2} - 5\) , \( -\frac{1}{4} a^{3} - \frac{3}{4} a^{2} + \frac{9}{4} a + 6\) , \( \frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{9}{4} a - 5\) , \( -\frac{39}{4} a^{3} + \frac{119}{4} a^{2} + \frac{43}{4} a - 44\) , \( \frac{267}{4} a^{3} - \frac{883}{4} a^{2} - \frac{415}{4} a + 498\bigr] \)	${y}^2+\left(a^{2}-5\right){x}{y}+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{9}{4}a-5\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}-\frac{3}{4}a^{2}+\frac{9}{4}a+6\right){x}^{2}+\left(-\frac{39}{4}a^{3}+\frac{119}{4}a^{2}+\frac{43}{4}a-44\right){x}+\frac{267}{4}a^{3}-\frac{883}{4}a^{2}-\frac{415}{4}a+498$
11.1-b4	11.1-b	$6$	$8$	4.4.7625.1	$4$	$[4, 0]$	11.1	\( 11 \)	\( 11 \)	$10.53010$	$(1/4a^3-1/4a^2-9/4a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$4$	\( 1 \)	$1$	$182.8597614$	2.094103896	\( \frac{7273468393095067}{22} a^{3} + \frac{14302897799889049}{22} a^{2} - \frac{2093855705464743}{2} a - \frac{19615292432376359}{11} \)	\( \bigl[\frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{5}{4} a\) , \( -\frac{1}{4} a^{3} + \frac{5}{4} a^{2} - \frac{3}{4} a - 6\) , \( a + 1\) , \( -\frac{111}{4} a^{3} - \frac{153}{4} a^{2} + \frac{335}{4} a + 116\) , \( \frac{1063}{4} a^{3} + \frac{2365}{4} a^{2} - \frac{3471}{4} a - 1594\bigr] \)	${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{5}{4}a\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}+\frac{5}{4}a^{2}-\frac{3}{4}a-6\right){x}^{2}+\left(-\frac{111}{4}a^{3}-\frac{153}{4}a^{2}+\frac{335}{4}a+116\right){x}+\frac{1063}{4}a^{3}+\frac{2365}{4}a^{2}-\frac{3471}{4}a-1594$

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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.