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
7.1-a2
7.1-a
$2$
$2$
4.4.8768.1
$4$
$[4, 0]$
7.1
\( 7 \)
\( 7^{8} \)
$10.67151$
$(-a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$155.3164161$
0.829348559
\( \frac{57165234770944}{5764801} a^{3} + \frac{29324092490688}{5764801} a^{2} - \frac{177134335713792}{5764801} a - \frac{137148082835392}{5764801} \)
\( \bigl[a^{2} - a - 3\) , \( a^{2} - a - 4\) , \( a^{2} - 2\) , \( 8 a^{3} - 30 a^{2} + 8 a + 34\) , \( -29 a^{3} + 103 a^{2} - 28 a - 118\bigr] \)
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(8a^{3}-30a^{2}+8a+34\right){x}-29a^{3}+103a^{2}-28a-118$
49.10-b2
49.10-b
$2$
$2$
4.4.8768.1
$4$
$[4, 0]$
49.10
\( 7^{2} \)
\( 7^{14} \)
$13.61016$
$(-a)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$0.971047582$
$72.43223032$
3.004568365
\( \frac{57165234770944}{5764801} a^{3} + \frac{29324092490688}{5764801} a^{2} - \frac{177134335713792}{5764801} a - \frac{137148082835392}{5764801} \)
\( \bigl[a^{3} - a^{2} - 3 a\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( a + 1\) , \( 6 a^{3} - 27 a^{2} + 19 a + 26\) , \( -54 a^{3} + 186 a^{2} + 3 a - 309\bigr] \)
${y}^2+\left(a^{3}-a^{2}-3a\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-1\right){x}^{2}+\left(6a^{3}-27a^{2}+19a+26\right){x}-54a^{3}+186a^{2}+3a-309$
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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.