Elliptic curves over 4.4.19821.1 of conductor 3.1

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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
3.1-a1	3.1-a	$2$	$11$	4.4.19821.1	$4$	$[4, 0]$	3.1	\( 3 \)	\( 3 \)	$14.43250$	$(-1/3a^3-1/3a^2+3a+2)$	$0 \le r \le 1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$11$	11B.1.2		\( 1 \)	$1$	$0.021714933$	2.780221650	\( -17320935403935602154 a^{3} + \frac{70045782250784531003}{3} a^{2} + \frac{391326656179292150729}{3} a - 149319306081545580681 \)	\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a\) , \( a\) , \( a^{2} - 4\) , \( \frac{20753}{3} a^{3} + \frac{2342}{3} a^{2} - 54658 a - 19596\) , \( \frac{2144189}{3} a^{3} + \frac{227318}{3} a^{2} - 5636519 a - 1948781\bigr] \)	${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+a{x}^{2}+\left(\frac{20753}{3}a^{3}+\frac{2342}{3}a^{2}-54658a-19596\right){x}+\frac{2144189}{3}a^{3}+\frac{227318}{3}a^{2}-5636519a-1948781$
3.1-a2	3.1-a	$2$	$11$	4.4.19821.1	$4$	$[4, 0]$	3.1	\( 3 \)	\( 3^{11} \)	$14.43250$	$(-1/3a^3-1/3a^2+3a+2)$	$0 \le r \le 1$	$\Z/11\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$11$	11B.1.1		\( 11 \)	$1$	$317.9283472$	2.780221650	\( -\frac{73343}{729} a^{3} + \frac{24131}{729} a^{2} + \frac{615892}{729} a + \frac{18719}{27} \)	\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a\) , \( a\) , \( a^{2} - 4\) , \( -\frac{7}{3} a^{3} + \frac{2}{3} a^{2} + 22 a + 9\) , \( -\frac{10}{3} a^{3} + \frac{5}{3} a^{2} + 32 a + 7\bigr] \)	${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+a{x}^{2}+\left(-\frac{7}{3}a^{3}+\frac{2}{3}a^{2}+22a+9\right){x}-\frac{10}{3}a^{3}+\frac{5}{3}a^{2}+32a+7$

 

  *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.