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
400.3-a3
400.3-a
$4$
$6$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
400.3
\( 2^{4} \cdot 5^{2} \)
\( 2^{8} \cdot 5^{2} \)
$1.05731$
$(a), (-a+1), (5)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B.1.1
$1$
\( 3^{2} \)
$1$
$6.423095656$
1.213850982
\( \frac{16384}{5} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 0\bigr] \)
${y}^2={x}^{3}+{x}^{2}-{x}$
6400.3-a3
6400.3-a
$4$
$6$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
6400.3
\( 2^{8} \cdot 5^{2} \)
\( 2^{14} \cdot 5^{2} \)
$2.11462$
$(a), (-a+1), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$1$
\( 2 \)
$1$
$4.541814495$
1.716644522
\( \frac{16384}{5} \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( -a + 2\) , \( 0\bigr] \)
${y}^2={x}^{3}-a{x}^{2}+\left(-a+2\right){x}$
6400.5-a3
6400.5-a
$4$
$6$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
6400.5
\( 2^{8} \cdot 5^{2} \)
\( 2^{8} \cdot 5^{2} \)
$2.11462$
$(a), (-a+1), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B
$1$
\( 1 \)
$1$
$6.423095656$
1.213850982
\( \frac{16384}{5} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( -1\) , \( 0\bigr] \)
${y}^2={x}^{3}-{x}^{2}-{x}$
6400.7-a3
6400.7-a
$4$
$6$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
6400.7
\( 2^{8} \cdot 5^{2} \)
\( 2^{14} \cdot 5^{2} \)
$2.11462$
$(a), (-a+1), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$1$
\( 2 \)
$1$
$4.541814495$
1.716644522
\( \frac{16384}{5} \)
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( a + 1\) , \( 0\bigr] \)
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(a+1\right){x}$
10000.3-a3
10000.3-a
$4$
$6$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
10000.3
\( 2^{4} \cdot 5^{4} \)
\( 2^{8} \cdot 5^{14} \)
$2.36422$
$(a), (-a+1), (5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$1.694375181$
$1.284619131$
3.290750365
\( \frac{16384}{5} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( -33\) , \( 62\bigr] \)
${y}^2={x}^{3}-{x}^{2}-33{x}+62$
25600.5-n3
25600.5-n
$4$
$6$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
25600.5
\( 2^{10} \cdot 5^{2} \)
\( 2^{14} \cdot 5^{2} \)
$2.99053$
$(a), (-a+1), (5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$1$
\( 2 \)
$1.490198062$
$4.541814495$
5.116280683
\( \frac{16384}{5} \)
\( \bigl[0\) , \( a\) , \( 0\) , \( -a + 2\) , \( 0\bigr] \)
${y}^2={x}^{3}+a{x}^{2}+\left(-a+2\right){x}$
25600.7-n3
25600.7-n
$4$
$6$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
25600.7
\( 2^{10} \cdot 5^{2} \)
\( 2^{14} \cdot 5^{2} \)
$2.99053$
$(a), (-a+1), (5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$1$
\( 2 \)
$1.490198062$
$4.541814495$
5.116280683
\( \frac{16384}{5} \)
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( a + 1\) , \( 0\bigr] \)
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(a+1\right){x}$
32400.3-a3
32400.3-a
$4$
$6$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
32400.3
\( 2^{4} \cdot 3^{4} \cdot 5^{2} \)
\( 2^{8} \cdot 3^{12} \cdot 5^{2} \)
$3.17193$
$(a), (-a+1), (3), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2^{2} \)
$1$
$2.141031885$
1.618467976
\( \frac{16384}{5} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -12\) , \( -11\bigr] \)
${y}^2={x}^{3}-12{x}-11$
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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.