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
3200.4-c3 3200.4-c $4$
$4$
\(\Q(\sqrt{-7}) \) $2$
$[0, 1]$
3200.4
\( 2^{7} \cdot 5^{2} \)
\( 2^{20} \cdot 5^{4} \)
$1.77818$
$(a), (-a+1), (5)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2Cs $1$
\( 2^{4} \)
$0.719148349$
$2.550556986$
2.773093359
\( \frac{19652}{25} \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a - 6\) , \( 6 a\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a-6\right){x}+6a$
3200.5-c3 3200.5-c $4$
$4$
\(\Q(\sqrt{-7}) \) $2$
$[0, 1]$
3200.5
\( 2^{7} \cdot 5^{2} \)
\( 2^{20} \cdot 5^{4} \)
$1.77818$
$(a), (-a+1), (5)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2Cs $1$
\( 2^{4} \)
$0.719148349$
$2.550556986$
2.773093359
\( \frac{19652}{25} \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a - 6\) , \( -6 a\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a-6\right){x}-6a$
12800.4-b3 12800.4-b $4$
$4$
\(\Q(\sqrt{-7}) \) $2$
$[0, 1]$
12800.4
\( 2^{9} \cdot 5^{2} \)
\( 2^{26} \cdot 5^{4} \)
$2.51472$
$(a), (-a+1), (5)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2Cs $1$
\( 2^{4} \)
$1$
$1.803516140$
1.363330055
\( \frac{19652}{25} \)
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -6 a + 11\) , \( 7 a - 13\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6a+11\right){x}+7a-13$
12800.7-b3 12800.7-b $4$
$4$
\(\Q(\sqrt{-7}) \) $2$
$[0, 1]$
12800.7
\( 2^{9} \cdot 5^{2} \)
\( 2^{26} \cdot 5^{4} \)
$2.51472$
$(a), (-a+1), (5)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2Cs $1$
\( 2^{4} \)
$1$
$1.803516140$
1.363330055
\( \frac{19652}{25} \)
\( \bigl[0\) , \( a\) , \( 0\) , \( 6 a + 5\) , \( -7 a - 6\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(6a+5\right){x}-7a-6$
25600.5-i3 25600.5-i $4$
$4$
\(\Q(\sqrt{-7}) \) $2$
$[0, 1]$
25600.5
\( 2^{10} \cdot 5^{2} \)
\( 2^{26} \cdot 5^{4} \)
$2.99053$
$(a), (-a+1), (5)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2Cs $1$
\( 2^{5} \)
$1$
$1.803516140$
2.726660110
\( \frac{19652}{25} \)
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -6 a + 11\) , \( -7 a + 13\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-6a+11\right){x}-7a+13$
25600.7-i3 25600.7-i $4$
$4$
\(\Q(\sqrt{-7}) \) $2$
$[0, 1]$
25600.7
\( 2^{10} \cdot 5^{2} \)
\( 2^{26} \cdot 5^{4} \)
$2.99053$
$(a), (-a+1), (5)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2Cs $1$
\( 2^{5} \)
$1$
$1.803516140$
2.726660110
\( \frac{19652}{25} \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( 6 a + 5\) , \( 7 a + 6\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(6a+5\right){x}+7a+6$
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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.
