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
7.3-a1
7.3-a
$2$
$3$
4.4.13888.1
$4$
$[4, 0]$
7.3
\( 7 \)
\( - 7^{3} \)
$13.43061$
$(-a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 1 \)
$1$
$223.0004007$
1.892281700
\( -\frac{294635720350}{1029} a^{3} - \frac{388473775936}{1029} a^{2} + \frac{773411784067}{1029} a + \frac{266343344894}{343} \)
\( \bigl[a + 1\) , \( 0\) , \( a^{2} - a - 3\) , \( -\frac{10}{3} a^{3} - \frac{19}{3} a^{2} + \frac{34}{3} a + 13\) , \( -30 a^{3} + 7 a^{2} + 49 a + 16\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(-\frac{10}{3}a^{3}-\frac{19}{3}a^{2}+\frac{34}{3}a+13\right){x}-30a^{3}+7a^{2}+49a+16$
7.3-b1
7.3-b
$2$
$3$
4.4.13888.1
$4$
$[4, 0]$
7.3
\( 7 \)
\( - 7^{3} \)
$13.43061$
$(-a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 3 \)
$0.012743831$
$2178.566117$
2.827041244
\( -\frac{294635720350}{1029} a^{3} - \frac{388473775936}{1029} a^{2} + \frac{773411784067}{1029} a + \frac{266343344894}{343} \)
\( \bigl[a^{2} - 4\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a^{2} - \frac{4}{3} a + 5\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{4}{3} a - 3\) , \( -\frac{11}{3} a^{3} + \frac{28}{3} a^{2} + \frac{44}{3} a - 34\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a^{2} - \frac{7}{3} a + 4\bigr] \)
${y}^2+\left(a^{2}-4\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{4}{3}a-3\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a^{2}-\frac{4}{3}a+5\right){x}^{2}+\left(-\frac{11}{3}a^{3}+\frac{28}{3}a^{2}+\frac{44}{3}a-34\right){x}+\frac{1}{3}a^{3}-\frac{5}{3}a^{2}-\frac{7}{3}a+4$
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Pari/GP
SageMath
Magma
Oscar
CSV
*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.