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
1250.3-a1
1250.3-a
$4$
$15$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
1250.3
\( 2 \cdot 5^{4} \)
\( 2^{6} \cdot 5^{8} \)
$1.06266$
$(a+1), (-a-2), (2a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3, 5$
3B.1.2 , 5B.1.3
$1$
\( 2 \)
$0.194697629$
$1.424166746$
1.109127558
\( -\frac{349938025}{8} \)
\( \bigl[i\) , \( 0\) , \( i\) , \( -125\) , \( 552\bigr] \)
${y}^2+i{x}{y}+i{y}={x}^{3}-125{x}+552$
1250.3-b1
1250.3-b
$4$
$15$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
1250.3
\( 2 \cdot 5^{4} \)
\( 2^{6} \cdot 5^{20} \)
$1.06266$
$(a+1), (-a-2), (2a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3, 5$
3B , 5B.1.2
$1$
\( 2 \cdot 3 \)
$1$
$0.284833349$
1.709000096
\( -\frac{349938025}{8} \)
\( \bigl[i\) , \( -1\) , \( i\) , \( -3137\) , \( 68969\bigr] \)
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}-3137{x}+68969$
10000.3-e1
10000.3-e
$4$
$15$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
10000.3
\( 2^{4} \cdot 5^{4} \)
\( 2^{18} \cdot 5^{14} \)
$1.78718$
$(a+1), (-a-2), (2a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3, 5$
3B , 5B.4.2
$1$
\( 2 \cdot 3 \)
$1$
$0.318453365$
1.910720194
\( -\frac{349938025}{8} \)
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( 2008 i - 1506\) , \( 48554 i - 8828\bigr] \)
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(2008i-1506\right){x}+48554i-8828$
10000.3-f1
10000.3-f
$4$
$15$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
10000.3
\( 2^{4} \cdot 5^{4} \)
\( 2^{18} \cdot 5^{14} \)
$1.78718$
$(a+1), (-a-2), (2a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3, 5$
3B , 5B.4.2
$1$
\( 2 \cdot 3 \)
$1$
$0.318453365$
1.910720194
\( -\frac{349938025}{8} \)
\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( -2008 i - 1506\) , \( -48554 i - 8828\bigr] \)
${y}^2+\left(i+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-2008i-1506\right){x}-48554i-8828$
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.