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
1156.2-a4 1156.2-a $4$
$6$
\(\Q(\sqrt{-7}) \) $2$
$[0, 1]$
1156.2
\( 2^{2} \cdot 17^{2} \)
\( 2^{4} \cdot 17^{6} \)
$1.37856$
$(a), (-a+1), (17)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$2, 3$
2B , 3B.1.2 $1$
\( 2^{2} \cdot 3 \)
$1$
$1.396783906$
3.167608159
\( \frac{120920208625}{19652} \)
\( \bigl[1\) , \( 0\) , \( 0\) , \( -103\) , \( -411\bigr] \) ${y}^2+{x}{y}={x}^{3}-103{x}-411$
36992.2-d4 36992.2-d $4$
$6$
\(\Q(\sqrt{-7}) \) $2$
$[0, 1]$
36992.2
\( 2^{7} \cdot 17^{2} \)
\( 2^{22} \cdot 17^{6} \)
$3.27880$
$(a), (-a+1), (17)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2, 3$
2B , 3B $1$
\( 2^{3} \cdot 3 \)
$1$
$0.493837686$
2.239837209
\( \frac{120920208625}{19652} \)
\( \bigl[a\) , \( 1\) , \( 0\) , \( -515 a - 206\) , \( -6987 a + 2466\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-515a-206\right){x}-6987a+2466$
36992.7-d4 36992.7-d $4$
$6$
\(\Q(\sqrt{-7}) \) $2$
$[0, 1]$
36992.7
\( 2^{7} \cdot 17^{2} \)
\( 2^{22} \cdot 17^{6} \)
$3.27880$
$(a), (-a+1), (17)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2, 3$
2B , 3B $1$
\( 2^{3} \cdot 3 \)
$1$
$0.493837686$
2.239837209
\( \frac{120920208625}{19652} \)
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 515 a - 721\) , \( 6987 a - 4521\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(515a-721\right){x}+6987a-4521$
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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.
