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
49.1-a2
49.1-a
$2$
$7$
6.6.1279733.1
$6$
$[6, 0]$
49.1
\( 7^{2} \)
\( - 7^{7} \)
$139.81311$
$(a^4-2a^3-3a^2+6a-1)$
$1$
$\Z/7\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$7$
7B.1.1[3]
$1$
\( 2 \)
$0.155016578$
$111773.5823$
3.75097
\( \frac{501548626}{7} a^{5} + \frac{166452530}{7} a^{4} - \frac{2621036258}{7} a^{3} - \frac{1096676327}{7} a^{2} + \frac{2456909923}{7} a + \frac{213445339}{7} \)
\( \bigl[a^{4} - a^{3} - 3 a^{2} + a\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 6 a^{2} - 4 a + 2\) , \( a^{5} - a^{4} - 3 a^{3} + 2 a^{2} - a\) , \( 4 a^{5} + a^{4} - 28 a^{3} - 2 a^{2} + 31 a - 23\) , \( -12 a^{5} + 3 a^{4} + 62 a^{3} + a^{2} - 46 a + 31\bigr] \)
${y}^2+\left(a^{4}-a^{3}-3a^{2}+a\right){x}{y}+\left(a^{5}-a^{4}-3a^{3}+2a^{2}-a\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+4a^{3}-6a^{2}-4a+2\right){x}^{2}+\left(4a^{5}+a^{4}-28a^{3}-2a^{2}+31a-23\right){x}-12a^{5}+3a^{4}+62a^{3}+a^{2}-46a+31$
49.1-f2
49.1-f
$2$
$7$
6.6.1279733.1
$6$
$[6, 0]$
49.1
\( 7^{2} \)
\( - 7^{7} \)
$139.81311$
$(a^4-2a^3-3a^2+6a-1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$7$
7B.6.1[3]
$1$
\( 2^{2} \)
$0.214179727$
$689.8768767$
3.13474
\( \frac{501548626}{7} a^{5} + \frac{166452530}{7} a^{4} - \frac{2621036258}{7} a^{3} - \frac{1096676327}{7} a^{2} + \frac{2456909923}{7} a + \frac{213445339}{7} \)
\( \bigl[a^{5} - 2 a^{4} - 3 a^{3} + 7 a^{2} - a - 3\) , \( -a^{5} + 3 a^{4} + a^{3} - 8 a^{2} + 3 a\) , \( 1\) , \( -4 a^{5} + 7 a^{4} + 21 a^{3} - 20 a^{2} - 39 a - 1\) , \( 6 a^{5} + 2 a^{4} - 65 a^{3} + 145 a + 12\bigr] \)
${y}^2+\left(a^{5}-2a^{4}-3a^{3}+7a^{2}-a-3\right){x}{y}+{y}={x}^{3}+\left(-a^{5}+3a^{4}+a^{3}-8a^{2}+3a\right){x}^{2}+\left(-4a^{5}+7a^{4}+21a^{3}-20a^{2}-39a-1\right){x}+6a^{5}+2a^{4}-65a^{3}+145a+12$
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.