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
2500.3-a2
2500.3-a
$4$
$15$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
2500.3
\( 2^{2} \cdot 5^{4} \)
\( 2^{10} \cdot 5^{4} \)
$2.09566$
$(-a-1), (a-2), (2)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3, 5$
3B , 5B.1.1
$1$
\( 5 \)
$1$
$4.272500240$
0.515282916
\( -\frac{121945}{32} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( -3\) , \( 1\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-3{x}+1$
2500.3-b2
2500.3-b
$4$
$15$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
2500.3
\( 2^{2} \cdot 5^{4} \)
\( 2^{10} \cdot 5^{10} \)
$2.09566$
$(-a-1), (a-2), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3, 5$
3B , 5B.4.1
$1$
\( 1 \)
$1$
$1.910720194$
1.152207629
\( -\frac{121945}{32} \)
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( -11 a + 7\) , \( 13 a - 18\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-11a+7\right){x}+13a-18$
2500.3-d2
2500.3-d
$4$
$15$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
2500.3
\( 2^{2} \cdot 5^{4} \)
\( 2^{10} \cdot 5^{10} \)
$2.09566$
$(-a-1), (a-2), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3, 5$
3B , 5B.4.1
$1$
\( 1 \)
$1$
$1.910720194$
1.152207629
\( -\frac{121945}{32} \)
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 8 a - 5\) , \( -9 a - 32\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(8a-5\right){x}-9a-32$
2500.3-h2
2500.3-h
$4$
$15$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
2500.3
\( 2^{2} \cdot 5^{4} \)
\( 2^{10} \cdot 5^{16} \)
$2.09566$
$(-a-1), (a-2), (2)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3, 5$
3B.1.1 , 5B.1.4
$1$
\( 3^{2} \cdot 5 \)
$1$
$0.854500048$
2.576414584
\( -\frac{121945}{32} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -76\) , \( 298\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-76{x}+298$
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.