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 $2$
$2$
4.4.9909.1 $4$
$[4, 0]$
3.1
\( 3 \)
\( 3^{8} \)
$10.20454$
$(-a^3+a^2+4a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2 \)
$1$
$140.0282857$
0.703348980
\( -357531767 a^{3} + \frac{3885538150}{9} a^{2} + \frac{14614849117}{9} a - \frac{7994350247}{9} \)
\( \bigl[a^{3} - 4 a - 2\) , \( a^{2} - 2 a - 2\) , \( a^{3} - 5 a - 1\) , \( 13 a^{3} - 28 a^{2} - 26 a + 32\) , \( -85 a^{3} + 160 a^{2} + 209 a - 133\bigr] \) ${y}^2+\left(a^{3}-4a-2\right){x}{y}+\left(a^{3}-5a-1\right){y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(13a^{3}-28a^{2}-26a+32\right){x}-85a^{3}+160a^{2}+209a-133$
3.1-a2 3.1-a $2$
$2$
4.4.9909.1 $4$
$[4, 0]$
3.1
\( 3 \)
\( 3^{4} \)
$10.20454$
$(-a^3+a^2+4a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2 \)
$1$
$140.0282857$
0.703348980
\( 568516610958557191 a^{3} - 686495379714342911 a^{2} - \frac{7746427564028264581}{3} a + \frac{4237319461104453760}{3} \)
\( \bigl[a + 1\) , \( -a^{2} + 2 a + 4\) , \( a^{2} - 3\) , \( 358 a^{3} + 180 a^{2} - 2067 a - 2129\) , \( 836 a^{3} + 427 a^{2} - 4792 a - 4938\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(358a^{3}+180a^{2}-2067a-2129\right){x}+836a^{3}+427a^{2}-4792a-4938$
3.1-b1 3.1-b $2$
$2$
4.4.9909.1 $4$
$[4, 0]$
3.1
\( 3 \)
\( 3^{4} \)
$10.20454$
$(-a^3+a^2+4a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2 \)
$1$
$269.1804840$
1.352068391
\( 568516610958557191 a^{3} - 686495379714342911 a^{2} - \frac{7746427564028264581}{3} a + \frac{4237319461104453760}{3} \)
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{3} + a^{2} + 3 a - 2\) , \( 0\) , \( 60 a^{3} + 24 a^{2} - 336 a - 336\) , \( -6 a^{3} - 33 a^{2} + 75 a + 129\bigr] \) ${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}={x}^{3}+\left(-a^{3}+a^{2}+3a-2\right){x}^{2}+\left(60a^{3}+24a^{2}-336a-336\right){x}-6a^{3}-33a^{2}+75a+129$
3.1-b2 3.1-b $2$
$2$
4.4.9909.1 $4$
$[4, 0]$
3.1
\( 3 \)
\( 3^{8} \)
$10.20454$
$(-a^3+a^2+4a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2 \)
$1$
$269.1804840$
1.352068391
\( -357531767 a^{3} + \frac{3885538150}{9} a^{2} + \frac{14614849117}{9} a - \frac{7994350247}{9} \)
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{3} + a^{2} + 3 a - 2\) , \( 0\) , \( -15 a^{3} - 6 a^{2} + 84 a + 84\) , \( 0\bigr] \) ${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}={x}^{3}+\left(-a^{3}+a^{2}+3a-2\right){x}^{2}+\left(-15a^{3}-6a^{2}+84a+84\right){x}$
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Pari/GP
SageMath
Magma
Oscar
CSV
*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.
