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
3136.2-a1
3136.2-a
$4$
$4$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
3136.2
\( 2^{6} \cdot 7^{2} \)
\( 2^{16} \cdot 7^{2} \)
$1.15823$
$(-3a+1), (3a-2), (2)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$4.016295718$
1.159404707
\( \frac{432}{7} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( a - 1\) , \( 2\bigr] \)
${y}^2={x}^{3}+\left(a-1\right){x}+2$
3136.2-a2
3136.2-a
$4$
$4$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
3136.2
\( 2^{6} \cdot 7^{2} \)
\( 2^{22} \cdot 7^{8} \)
$1.15823$
$(-3a+1), (3a-2), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$1.004073929$
1.159404707
\( \frac{11090466}{2401} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -59 a + 59\) , \( -138\bigr] \)
${y}^2={x}^{3}+\left(-59a+59\right){x}-138$
3136.2-a3
3136.2-a
$4$
$4$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
3136.2
\( 2^{6} \cdot 7^{2} \)
\( 2^{20} \cdot 7^{4} \)
$1.15823$
$(-3a+1), (3a-2), (2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$2.008147859$
1.159404707
\( \frac{740772}{49} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -19 a + 19\) , \( 30\bigr] \)
${y}^2={x}^{3}+\left(-19a+19\right){x}+30$
3136.2-a4
3136.2-a
$4$
$4$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
3136.2
\( 2^{6} \cdot 7^{2} \)
\( 2^{22} \cdot 7^{2} \)
$1.15823$
$(-3a+1), (3a-2), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$4$
\( 1 \)
$1$
$1.004073929$
1.159404707
\( \frac{1443468546}{7} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -299 a + 299\) , \( 1990\bigr] \)
${y}^2={x}^{3}+\left(-299a+299\right){x}+1990$
3136.2-b1
3136.2-b
$2$
$2$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
3136.2
\( 2^{6} \cdot 7^{2} \)
\( 2^{20} \cdot 7^{2} \)
$1.15823$
$(-3a+1), (3a-2), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2 \)
$1$
$3.197869643$
1.846290899
\( -\frac{4}{7} \)
\( \bigl[0\) , \( a\) , \( 0\) , \( 0\) , \( -4\bigr] \)
${y}^2={x}^{3}+a{x}^{2}-4$
3136.2-b2
3136.2-b
$2$
$2$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
3136.2
\( 2^{6} \cdot 7^{2} \)
\( 2^{22} \cdot 7^{4} \)
$1.15823$
$(-3a+1), (3a-2), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$1.598934821$
1.846290899
\( \frac{3543122}{49} \)
\( \bigl[0\) , \( a\) , \( 0\) , \( -40 a + 40\) , \( -84\bigr] \)
${y}^2={x}^{3}+a{x}^{2}+\left(-40a+40\right){x}-84$
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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.