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
91.1-a2
91.1-a
$8$
$16$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
91.1
\( 7 \cdot 13 \)
\( 7 \cdot 13^{2} \)
$1.32661$
$(-a^2-a+2), (-2a^2+a+2)$
0
$\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$145.8010047$
0.650897342
\( -\frac{929922096412289245}{1183} a^{2} + \frac{516067794318659937}{1183} a + \frac{2089516047340720303}{1183} \)
\( \bigl[a^{2} - 2\) , \( a^{2} - 3\) , \( 0\) , \( 15 a^{2} + 5 a - 89\) , \( -89 a^{2} - 20 a + 385\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(15a^{2}+5a-89\right){x}-89a^{2}-20a+385$
637.3-a2
637.3-a
$8$
$16$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
637.3
\( 7^{2} \cdot 13 \)
\( 7^{7} \cdot 13^{2} \)
$1.83482$
$(-a^2-a+2), (-2a^2+a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$4$
\( 2^{2} \)
$1$
$1.961908819$
1.121090754
\( -\frac{929922096412289245}{1183} a^{2} + \frac{516067794318659937}{1183} a + \frac{2089516047340720303}{1183} \)
\( \bigl[a^{2} + a - 1\) , \( -a^{2} + 3\) , \( a + 1\) , \( -229 a^{2} + 409 a - 182\) , \( -2858 a^{2} + 5655 a - 2125\bigr] \)
${y}^2+\left(a^{2}+a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-229a^{2}+409a-182\right){x}-2858a^{2}+5655a-2125$
1183.5-c3
1183.5-c
$8$
$16$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
1183.5
\( 7 \cdot 13^{2} \)
\( 7 \cdot 13^{8} \)
$2.03423$
$(-a^2-a+2), (-2a^2+a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$4$
\( 2 \)
$1$
$4.199091953$
1.199740558
\( -\frac{929922096412289245}{1183} a^{2} + \frac{516067794318659937}{1183} a + \frac{2089516047340720303}{1183} \)
\( \bigl[a + 1\) , \( 1\) , \( a^{2} + a - 1\) , \( -383 a^{2} + 831 a - 403\) , \( 6736 a^{2} - 15370 a + 5006\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+{x}^{2}+\left(-383a^{2}+831a-403\right){x}+6736a^{2}-15370a+5006$
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.