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
1600.4-a2
1600.4-a
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
1600.4
\( 2^{6} \cdot 5^{2} \)
\( 2^{16} \cdot 5^{4} \)
$1.49526$
$(a), (-a+1), (5)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$2.996888981$
1.132717564
\( \frac{148176}{25} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( -6\bigr] \)
${y}^2={x}^{3}-7{x}-6$
6400.5-b2
6400.5-b
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
6400.5
\( 2^{8} \cdot 5^{2} \)
\( 2^{16} \cdot 5^{4} \)
$2.11462$
$(a), (-a+1), (5)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$2.996888981$
1.132717564
\( \frac{148176}{25} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 6\bigr] \)
${y}^2={x}^{3}-7{x}+6$
12800.4-g2
12800.4-g
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
12800.4
\( 2^{9} \cdot 5^{2} \)
\( 2^{22} \cdot 5^{4} \)
$2.51472$
$(a), (-a+1), (5)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{5} \)
$1$
$2.119120521$
3.203809084
\( \frac{148176}{25} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7 a + 14\) , \( -6 a - 12\bigr] \)
${y}^2={x}^{3}+\left(-7a+14\right){x}-6a-12$
12800.7-g2
12800.7-g
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
12800.7
\( 2^{9} \cdot 5^{2} \)
\( 2^{22} \cdot 5^{4} \)
$2.51472$
$(a), (-a+1), (5)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{5} \)
$1$
$2.119120521$
3.203809084
\( \frac{148176}{25} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 7 a + 7\) , \( 6 a - 18\bigr] \)
${y}^2={x}^{3}+\left(7a+7\right){x}+6a-18$
25600.5-c2
25600.5-c
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
25600.5
\( 2^{10} \cdot 5^{2} \)
\( 2^{22} \cdot 5^{4} \)
$2.99053$
$(a), (-a+1), (5)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{4} \)
$1$
$2.119120521$
1.601904542
\( \frac{148176}{25} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7 a + 14\) , \( 6 a + 12\bigr] \)
${y}^2={x}^{3}+\left(-7a+14\right){x}+6a+12$
25600.7-c2
25600.7-c
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
25600.7
\( 2^{10} \cdot 5^{2} \)
\( 2^{22} \cdot 5^{4} \)
$2.99053$
$(a), (-a+1), (5)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{4} \)
$1$
$2.119120521$
1.601904542
\( \frac{148176}{25} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 7 a + 7\) , \( -6 a + 18\bigr] \)
${y}^2={x}^{3}+\left(7a+7\right){x}-6a+18$
40000.4-e2
40000.4-e
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
40000.4
\( 2^{6} \cdot 5^{4} \)
\( 2^{16} \cdot 5^{16} \)
$3.34351$
$(a), (-a+1), (5)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{6} \)
$1.578365660$
$0.599377796$
5.721096022
\( \frac{148176}{25} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -175\) , \( -750\bigr] \)
${y}^2={x}^{3}-175{x}-750$
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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.