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
49.2-a1
49.2-a
$4$
$10$
4.4.4205.1
$4$
$[4, 0]$
49.2
\( 7^{2} \)
\( 7^{20} \)
$9.42532$
$(-a^3+2a^2+3a-3), (a^2-2a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 5$
2B , 5B.4.1
$1$
\( 2^{2} \)
$1$
$102.9191920$
1.587133170
\( \frac{91176666325}{282475249} a^{3} - \frac{91176666325}{282475249} a^{2} - \frac{547059997950}{282475249} a + \frac{199910878122}{282475249} \)
\( \bigl[a^{3} - a^{2} - 4 a - 1\) , \( 0\) , \( 0\) , \( -4 a^{3} + 4 a^{2} + 24 a - 8\) , \( -a^{3} + a^{2} + 6 a - 1\bigr] \)
${y}^2+\left(a^{3}-a^{2}-4a-1\right){x}{y}={x}^{3}+\left(-4a^{3}+4a^{2}+24a-8\right){x}-a^{3}+a^{2}+6a-1$
343.3-d4
343.3-d
$4$
$10$
4.4.4205.1
$4$
$[4, 0]$
343.3
\( 7^{3} \)
\( 7^{26} \)
$12.02080$
$(-a^3+2a^2+3a-3), (a^2-2a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 5$
2B , 5B.4.1
$1$
\( 2^{3} \cdot 5 \)
$1$
$13.08439948$
2.017765978
\( \frac{91176666325}{282475249} a^{3} - \frac{91176666325}{282475249} a^{2} - \frac{547059997950}{282475249} a + \frac{199910878122}{282475249} \)
\( \bigl[a^{3} - a^{2} - 4 a\) , \( a^{3} - a^{2} - 5 a - 1\) , \( -a^{3} + 2 a^{2} + 3 a\) , \( -2 a^{3} - 5 a^{2} + a + 3\) , \( -4140 a^{3} - 7622 a^{2} - 946 a + 1456\bigr] \)
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(-a^{3}+2a^{2}+3a\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a-1\right){x}^{2}+\left(-2a^{3}-5a^{2}+a+3\right){x}-4140a^{3}-7622a^{2}-946a+1456$
343.4-d1
343.4-d
$4$
$10$
4.4.4205.1
$4$
$[4, 0]$
343.4
\( 7^{3} \)
\( 7^{26} \)
$12.02080$
$(-a^3+2a^2+3a-3), (a^2-2a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 5$
2B , 5B.4.1
$1$
\( 2^{3} \cdot 5 \)
$1$
$13.08439948$
2.017765978
\( \frac{91176666325}{282475249} a^{3} - \frac{91176666325}{282475249} a^{2} - \frac{547059997950}{282475249} a + \frac{199910878122}{282475249} \)
\( \bigl[a^{2} - a - 1\) , \( 2 a^{3} - 3 a^{2} - 9 a\) , \( a^{3} - a^{2} - 5 a\) , \( 3 a^{3} - 7 a^{2} - 7 a + 4\) , \( 44 a^{3} - 82 a^{2} - 339 a - 173\bigr] \)
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{3}-a^{2}-5a\right){y}={x}^{3}+\left(2a^{3}-3a^{2}-9a\right){x}^{2}+\left(3a^{3}-7a^{2}-7a+4\right){x}+44a^{3}-82a^{2}-339a-173$
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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.