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 $1$
$1$
4.4.19429.1 $4$
$[4, 0]$
3.1
\( 3 \)
\( 3^{3} \)
$14.28907$
$(a^3-a^2-6a-3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$1$
\( 1 \)
$1$
$233.0832829$
1.672191079
\( -\frac{46448}{27} a^{3} - \frac{6578}{9} a^{2} + \frac{120947}{27} a - \frac{52073}{27} \)
\( \bigl[a^{2} - a - 4\) , \( -a^{3} + a^{2} + 4 a + 3\) , \( 0\) , \( -2 a^{3} - 2 a^{2} + 20 a + 24\) , \( 2 a^{3} - 15 a^{2} + 14 a + 41\bigr] \) ${y}^2+\left(a^{2}-a-4\right){x}{y}={x}^{3}+\left(-a^{3}+a^{2}+4a+3\right){x}^{2}+\left(-2a^{3}-2a^{2}+20a+24\right){x}+2a^{3}-15a^{2}+14a+41$
3.1-b1 3.1-b $1$
$1$
4.4.19429.1 $4$
$[4, 0]$
3.1
\( 3 \)
\( 3^{13} \)
$14.28907$
$(a^3-a^2-6a-3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$1$
\( 1 \)
$1$
$132.9092858$
0.953520644
\( -\frac{554873342}{1594323} a^{3} + \frac{311661553}{531441} a^{2} + \frac{2398493765}{1594323} a + \frac{609744973}{1594323} \)
\( \bigl[a^{3} - 2 a^{2} - 4 a + 2\) , \( a^{3} - a^{2} - 5 a - 2\) , \( a^{3} - a^{2} - 5 a - 1\) , \( -8 a^{3} + 2 a^{2} + 58 a + 52\) , \( 13 a^{3} - 3 a^{2} - 94 a - 86\bigr] \) ${y}^2+\left(a^{3}-2a^{2}-4a+2\right){x}{y}+\left(a^{3}-a^{2}-5a-1\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a-2\right){x}^{2}+\left(-8a^{3}+2a^{2}+58a+52\right){x}+13a^{3}-3a^{2}-94a-86$
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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.
