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-a1
1600.4-a
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
1600.4
\( 2^{6} \cdot 5^{2} \)
\( 2^{20} \cdot 5^{8} \)
$1.49526$
$(a), (-a+1), (5)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{4} \)
$1$
$1.498444490$
1.132717564
\( \frac{237276}{625} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \)
${y}^2={x}^{3}+13{x}-34$
6400.5-b1
6400.5-b
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
6400.5
\( 2^{8} \cdot 5^{2} \)
\( 2^{20} \cdot 5^{8} \)
$2.11462$
$(a), (-a+1), (5)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{4} \)
$1$
$1.498444490$
1.132717564
\( \frac{237276}{625} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( 34\bigr] \)
${y}^2={x}^{3}+13{x}+34$
12800.4-g1
12800.4-g
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
12800.4
\( 2^{9} \cdot 5^{2} \)
\( 2^{26} \cdot 5^{8} \)
$2.51472$
$(a), (-a+1), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{4} \)
$1$
$1.059560260$
3.203809084
\( \frac{237276}{625} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13 a - 26\) , \( -34 a - 68\bigr] \)
${y}^2={x}^{3}+\left(13a-26\right){x}-34a-68$
12800.7-g1
12800.7-g
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
12800.7
\( 2^{9} \cdot 5^{2} \)
\( 2^{26} \cdot 5^{8} \)
$2.51472$
$(a), (-a+1), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{4} \)
$1$
$1.059560260$
3.203809084
\( \frac{237276}{625} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -13 a - 13\) , \( 34 a - 102\bigr] \)
${y}^2={x}^{3}+\left(-13a-13\right){x}+34a-102$
25600.5-c1
25600.5-c
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
25600.5
\( 2^{10} \cdot 5^{2} \)
\( 2^{26} \cdot 5^{8} \)
$2.99053$
$(a), (-a+1), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{3} \)
$1$
$1.059560260$
1.601904542
\( \frac{237276}{625} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13 a - 26\) , \( 34 a + 68\bigr] \)
${y}^2={x}^{3}+\left(13a-26\right){x}+34a+68$
25600.7-c1
25600.7-c
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
25600.7
\( 2^{10} \cdot 5^{2} \)
\( 2^{26} \cdot 5^{8} \)
$2.99053$
$(a), (-a+1), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{3} \)
$1$
$1.059560260$
1.601904542
\( \frac{237276}{625} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -13 a - 13\) , \( -34 a + 102\bigr] \)
${y}^2={x}^{3}+\left(-13a-13\right){x}-34a+102$
40000.4-e1
40000.4-e
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
40000.4
\( 2^{6} \cdot 5^{4} \)
\( 2^{20} \cdot 5^{20} \)
$3.34351$
$(a), (-a+1), (5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{4} \)
$3.156731320$
$0.299688898$
5.721096022
\( \frac{237276}{625} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 325\) , \( -4250\bigr] \)
${y}^2={x}^{3}+325{x}-4250$
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Pari/GP
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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.