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
9216.6-a2 9216.6-a $4$
$4$
\(\Q(\sqrt{-7}) \) $2$
$[0, 1]$
9216.6
\( 2^{10} \cdot 3^{2} \)
\( 2^{12} \cdot 3^{4} \)
$2.31645$
$(a), (-a+1), (3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2$
2Cs $1$
\( 2^{3} \)
$1$
$4.690728597$
1.772928762
\( \frac{21952}{9} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( -2\) , \( 0\bigr] \) ${y}^2={x}^{3}+{x}^{2}-2{x}$
9216.6-d2 9216.6-d $4$
$4$
\(\Q(\sqrt{-7}) \) $2$
$[0, 1]$
9216.6
\( 2^{10} \cdot 3^{2} \)
\( 2^{12} \cdot 3^{4} \)
$2.31645$
$(a), (-a+1), (3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2$
2Cs $1$
\( 2^{3} \)
$1$
$4.690728597$
1.772928762
\( \frac{21952}{9} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( -2\) , \( 0\bigr] \) ${y}^2={x}^{3}-{x}^{2}-2{x}$
18432.6-a2 18432.6-a $4$
$4$
\(\Q(\sqrt{-7}) \) $2$
$[0, 1]$
18432.6
\( 2^{11} \cdot 3^{2} \)
\( 2^{18} \cdot 3^{4} \)
$2.75474$
$(a), (-a+1), (3)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2Cs $1$
\( 2^{4} \)
$0.699969091$
$3.316845999$
3.510064866
\( \frac{21952}{9} \)
\( \bigl[0\) , \( a\) , \( 0\) , \( -2 a + 4\) , \( 0\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-2a+4\right){x}$
18432.6-j2 18432.6-j $4$
$4$
\(\Q(\sqrt{-7}) \) $2$
$[0, 1]$
18432.6
\( 2^{11} \cdot 3^{2} \)
\( 2^{18} \cdot 3^{4} \)
$2.75474$
$(a), (-a+1), (3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2Cs $1$
\( 2^{4} \)
$1$
$3.316845999$
2.507299900
\( \frac{21952}{9} \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( -2 a + 4\) , \( 0\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-2a+4\right){x}$
18432.7-c2 18432.7-c $4$
$4$
\(\Q(\sqrt{-7}) \) $2$
$[0, 1]$
18432.7
\( 2^{11} \cdot 3^{2} \)
\( 2^{18} \cdot 3^{4} \)
$2.75474$
$(a), (-a+1), (3)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2Cs $1$
\( 2^{4} \)
$0.699969091$
$3.316845999$
3.510064866
\( \frac{21952}{9} \)
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 2 a + 2\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a+2\right){x}$
18432.7-h2 18432.7-h $4$
$4$
\(\Q(\sqrt{-7}) \) $2$
$[0, 1]$
18432.7
\( 2^{11} \cdot 3^{2} \)
\( 2^{18} \cdot 3^{4} \)
$2.75474$
$(a), (-a+1), (3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2Cs $1$
\( 2^{4} \)
$1$
$3.316845999$
2.507299900
\( \frac{21952}{9} \)
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 2 a + 2\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(2a+2\right){x}$
36864.7-c2 36864.7-c $4$
$4$
\(\Q(\sqrt{-7}) \) $2$
$[0, 1]$
36864.7
\( 2^{12} \cdot 3^{2} \)
\( 2^{24} \cdot 3^{4} \)
$3.27596$
$(a), (-a+1), (3)$
$2$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2$
2Cs $1$
\( 2^{5} \)
$0.457259882$
$2.345364298$
6.485513576
\( \frac{21952}{9} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( -9\) , \( 9\bigr] \) ${y}^2={x}^{3}-{x}^{2}-9{x}+9$
36864.7-bb2 36864.7-bb $4$
$4$
\(\Q(\sqrt{-7}) \) $2$
$[0, 1]$
36864.7
\( 2^{12} \cdot 3^{2} \)
\( 2^{24} \cdot 3^{4} \)
$3.27596$
$(a), (-a+1), (3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2$
2Cs $1$
\( 2^{5} \)
$1$
$2.345364298$
3.545857524
\( \frac{21952}{9} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( -9\) , \( -9\bigr] \) ${y}^2={x}^{3}+{x}^{2}-9{x}-9$
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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.
