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
8.1-c3
8.1-c
$4$
$10$
3.3.733.1
$3$
$[3, 0]$
8.1
\( 2^{3} \)
\( - 2^{14} \)
$3.42141$
$(a^2-6), (a^2+a-3)$
0
$\Z/10\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.1
$1$
\( 2^{2} \cdot 5 \)
$1$
$135.7068839$
1.002489625
\( -\frac{229488321}{1024} a^{2} - \frac{40784951}{1024} a + \frac{1560076799}{1024} \)
\( \bigl[1\) , \( -a^{2} + a + 4\) , \( a\) , \( a^{2} - 3 a - 3\) , \( -a^{2} + a + 1\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(a^{2}-3a-3\right){x}-a^{2}+a+1$
64.3-g2
64.3-g
$4$
$10$
3.3.733.1
$3$
$[3, 0]$
64.3
\( 2^{6} \)
\( - 2^{26} \)
$4.83861$
$(a^2-6), (a^2+a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 5$
2B , 5B.4.1
$1$
\( 2^{2} \)
$1$
$74.72247810$
2.759937701
\( -\frac{229488321}{1024} a^{2} - \frac{40784951}{1024} a + \frac{1560076799}{1024} \)
\( \bigl[a^{2} + a - 4\) , \( a^{2} + a - 6\) , \( a\) , \( 30 a^{2} + 8 a - 191\) , \( -151 a^{2} - 22 a + 1036\bigr] \)
${y}^2+\left(a^{2}+a-4\right){x}{y}+a{y}={x}^{3}+\left(a^{2}+a-6\right){x}^{2}+\left(30a^{2}+8a-191\right){x}-151a^{2}-22a+1036$
200.3-c1
200.3-c
$4$
$10$
3.3.733.1
$3$
$[3, 0]$
200.3
\( 2^{3} \cdot 5^{2} \)
\( - 2^{14} \cdot 5^{6} \)
$5.85053$
$(a^2-6), (-a+3), (a^2+a-3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 5$
2B , 5B.4.1
$1$
\( 2^{3} \cdot 5 \)
$0.210859611$
$30.06363413$
7.024317722
\( -\frac{229488321}{1024} a^{2} - \frac{40784951}{1024} a + \frac{1560076799}{1024} \)
\( \bigl[a^{2} - 5\) , \( -a^{2} + a + 5\) , \( 1\) , \( -79 a^{2} - 116 a + 265\) , \( -311 a^{2} - 471 a + 989\bigr] \)
${y}^2+\left(a^{2}-5\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(-79a^{2}-116a+265\right){x}-311a^{2}-471a+989$
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.