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
49.4-a1
49.4-a
$2$
$7$
4.4.4205.1
$4$
$[4, 0]$
49.4
\( 7^{2} \)
\( - 7^{2} \)
$9.42532$
$(-a^3+2a^2+3a-3)$
$0 \le r \le 1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$7$
7B.1.3
\( 1 \)
$1$
$3.842943563$
2.266172452
\( -156521478494 a^{3} + 257550722470 a^{2} + 616417035615 a - 241680788762 \)
\( \bigl[a^{2} - a - 2\) , \( -2 a^{3} + 3 a^{2} + 9 a - 1\) , \( a\) , \( -24 a^{2} - 24 a + 1\) , \( -50 a^{3} - 134 a^{2} - 61 a\bigr] \)
${y}^2+\left(a^{2}-a-2\right){x}{y}+a{y}={x}^{3}+\left(-2a^{3}+3a^{2}+9a-1\right){x}^{2}+\left(-24a^{2}-24a+1\right){x}-50a^{3}-134a^{2}-61a$
49.4-c1
49.4-c
$2$
$7$
4.4.4205.1
$4$
$[4, 0]$
49.4
\( 7^{2} \)
\( - 7^{8} \)
$9.42532$
$(-a^3+2a^2+3a-3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$7$
7B.6.3
$1$
\( 1 \)
$1$
$85.38104876$
1.316674682
\( -156521478494 a^{3} + 257550722470 a^{2} + 616417035615 a - 241680788762 \)
\( \bigl[a^{3} - a^{2} - 4 a - 1\) , \( -2 a^{3} + 3 a^{2} + 8 a + 1\) , \( a + 1\) , \( 66 a^{3} - 37 a^{2} - 364 a - 233\) , \( -457 a^{3} + 318 a^{2} + 2384 a + 1238\bigr] \)
${y}^2+\left(a^{3}-a^{2}-4a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-2a^{3}+3a^{2}+8a+1\right){x}^{2}+\left(66a^{3}-37a^{2}-364a-233\right){x}-457a^{3}+318a^{2}+2384a+1238$
Download
displayed columns for
results
to
Text
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.