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
7.4-a1
7.4-a
$2$
$2$
4.4.8768.1
$4$
$[4, 0]$
7.4
\( 7 \)
\( 7^{8} \)
$10.67151$
$(-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$155.3164161$
0.829348559
\( -\frac{57165234770944}{5764801} a^{3} + \frac{200819796803520}{5764801} a^{2} - \frac{53009553580416}{5764801} a - \frac{32541870183936}{823543} \)
\( \bigl[a^{2} - a - 3\) , \( a^{2} - a - 4\) , \( a^{2} - 3\) , \( -9 a^{3} - 4 a^{2} + 30 a + 17\) , \( 28 a^{3} + 18 a^{2} - 90 a - 74\bigr] \)
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-9a^{3}-4a^{2}+30a+17\right){x}+28a^{3}+18a^{2}-90a-74$
49.7-b1
49.7-b
$2$
$2$
4.4.8768.1
$4$
$[4, 0]$
49.7
\( 7^{2} \)
\( 7^{14} \)
$13.61016$
$(-a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$0.971047582$
$72.43223032$
3.004568365
\( -\frac{57165234770944}{5764801} a^{3} + \frac{200819796803520}{5764801} a^{2} - \frac{53009553580416}{5764801} a - \frac{32541870183936}{823543} \)
\( \bigl[a^{3} - 4 a - 3\) , \( a^{3} - 2 a^{2} - 3 a + 4\) , \( a^{2} - 3\) , \( -7 a^{3} - 3 a^{2} + 18 a + 6\) , \( 36 a^{3} + 8 a^{2} - 163 a - 128\bigr] \)
${y}^2+\left(a^{3}-4a-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+4\right){x}^{2}+\left(-7a^{3}-3a^{2}+18a+6\right){x}+36a^{3}+8a^{2}-163a-128$
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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.