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
9.3-a1 9.3-a $3$
$9$
3.3.321.1 $3$
$[3, 0]$
9.3
\( 3^{2} \)
\( - 3^{15} \)
$2.30904$
$(a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ $3$
3B.1.2 $1$
\( 2 \)
$1$
$10.01686977$
1.118174302
\( -\frac{693022720}{19683} a^{2} - \frac{855752704}{19683} a + \frac{246431744}{19683} \)
\( \bigl[0\) , \( a^{2} - a - 2\) , \( a^{2} - 3\) , \( -708 a^{2} - 719 a + 214\) , \( -19813 a^{2} - 25500 a + 7228\bigr] \) ${y}^2+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-708a^{2}-719a+214\right){x}-19813a^{2}-25500a+7228$
9.3-a2 9.3-a $3$
$9$
3.3.321.1 $3$
$[3, 0]$
9.3
\( 3^{2} \)
\( - 3^{7} \)
$2.30904$
$(a+1)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ $3$
3B.1.1 $1$
\( 2 \)
$1$
$90.15182800$
1.118174302
\( \frac{1074386927992107008}{3} a^{2} - \frac{817476003654639616}{3} a - \frac{4493025253858410496}{3} \)
\( \bigl[0\) , \( a^{2} - a - 2\) , \( a + 1\) , \( 2 a^{2} - 38 a - 70\) , \( 73 a^{2} + 280 a + 265\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(2a^{2}-38a-70\right){x}+73a^{2}+280a+265$
9.3-a3 9.3-a $3$
$9$
3.3.321.1 $3$
$[3, 0]$
9.3
\( 3^{2} \)
\( - 3^{9} \)
$2.30904$
$(a+1)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ $3$
3Cs.1.1 $1$
\( 2 \)
$1$
$90.15182800$
1.118174302
\( \frac{7245824}{27} a^{2} - \frac{5521408}{27} a - \frac{30269440}{27} \)
\( \bigl[0\) , \( -a - 1\) , \( a^{2} - a - 3\) , \( 2354 a^{2} + 3433 a - 955\) , \( -230385 a^{2} - 336480 a + 93631\bigr] \) ${y}^2+\left(a^{2}-a-3\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2354a^{2}+3433a-955\right){x}-230385a^{2}-336480a+93631$
9.3-b1 9.3-b $2$
$3$
3.3.321.1 $3$
$[3, 0]$
9.3
\( 3^{2} \)
\( - 3^{3} \)
$2.30904$
$(a+1)$
$1$
$\mathsf{trivial}$
$\textsf{potential}$
$-3$
$N(\mathrm{U}(1))$ ✓
✓
$1$
\( 2 \)
$0.015440669$
$148.8699425$
0.769789308
\( 0 \)
\( \bigl[0\) , \( a^{2} - 4\) , \( 1\) , \( -a^{2} + a + 5\) , \( -a - 2\bigr] \) ${y}^2+{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-a^{2}+a+5\right){x}-a-2$
9.3-b2 9.3-b $2$
$3$
3.3.321.1 $3$
$[3, 0]$
9.3
\( 3^{2} \)
\( - 3^{9} \)
$2.30904$
$(a+1)$
$1$
$\mathsf{trivial}$
$\textsf{potential}$
$-3$
$N(\mathrm{U}(1))$ ✓
✓
$1$
\( 2 \)
$0.046322007$
$49.62331419$
0.769789308
\( 0 \)
\( \bigl[0\) , \( a^{2} - 4\) , \( a + 1\) , \( -a^{2} + a + 5\) , \( 67166 a^{2} + 98095 a - 27300\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-a^{2}+a+5\right){x}+67166a^{2}+98095a-27300$
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Pari/GP
SageMath
Magma
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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.
