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-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
\( -\frac{73343}{729} a^{3} + \frac{24131}{729} a^{2} + \frac{615892}{729} a + \frac{18719}{27} \)
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a\) , \( a\) , \( a^{2} - 4\) , \( -\frac{7}{3} a^{3} + \frac{2}{3} a^{2} + 22 a + 9\) , \( -\frac{10}{3} a^{3} + \frac{5}{3} a^{2} + 32 a + 7\bigr] \) ${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+a{x}^{2}+\left(-\frac{7}{3}a^{3}+\frac{2}{3}a^{2}+22a+9\right){x}-\frac{10}{3}a^{3}+\frac{5}{3}a^{2}+32a+7$
9.1-a2 9.1-a $2$
$11$
4.4.19821.1 $4$
$[4, 0]$
9.1
\( 3^{2} \)
\( 3^{17} \)
$16.55700$
$(-1/3a^3-1/3a^2+3a+2)$
$0 \le r \le 1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ $11$
11B.10.1 \( 2 \)
$1$
$141.1603238$
3.742242954
\( -\frac{73343}{729} a^{3} + \frac{24131}{729} a^{2} + \frac{615892}{729} a + \frac{18719}{27} \)
\( \bigl[a^{2} - 4\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 4 a\) , \( a^{2} - 4\) , \( -a^{3} + 3 a^{2} + 8 a + 4\) , \( 3 a^{3} + 8 a^{2} - 11 a - 3\bigr] \) ${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-4a\right){x}^{2}+\left(-a^{3}+3a^{2}+8a+4\right){x}+3a^{3}+8a^{2}-11a-3$
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Pari/GP
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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.
