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-a4
1250.3-a
$4$
$15$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
1250.3
\( 2 \cdot 5^{4} \)
\( 2^{30} \cdot 5^{16} \)
$1.06266$
$(a+1), (-a-2), (2a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3, 5$
3B.1.2 , 5B.1.4
$1$
\( 2 \)
$0.973488147$
$0.284833349$
1.109127558
\( \frac{46969655}{32768} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( 549\) , \( -2202\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+549{x}-2202$
1250.3-b4
1250.3-b
$4$
$15$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
1250.3
\( 2 \cdot 5^{4} \)
\( 2^{30} \cdot 5^{4} \)
$1.06266$
$(a+1), (-a-2), (2a+1)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3, 5$
3B , 5B.1.1
$1$
\( 2 \cdot 3 \cdot 5 \)
$1$
$1.424166746$
1.709000096
\( \frac{46969655}{32768} \)
\( \bigl[i\) , \( -1\) , \( i\) , \( 23\) , \( 9\bigr] \)
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}+23{x}+9$
10000.3-e4
10000.3-e
$4$
$15$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
10000.3
\( 2^{4} \cdot 5^{4} \)
\( 2^{42} \cdot 5^{10} \)
$1.78718$
$(a+1), (-a-2), (2a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3, 5$
3B , 5B.4.1
$1$
\( 2 \cdot 3 \)
$1$
$0.318453365$
1.910720194
\( \frac{46969655}{32768} \)
\( \bigl[i + 1\) , \( -i - 1\) , \( i + 1\) , \( 351 i + 264\) , \( -1744 i - 317\bigr] \)
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(351i+264\right){x}-1744i-317$
10000.3-f4
10000.3-f
$4$
$15$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
10000.3
\( 2^{4} \cdot 5^{4} \)
\( 2^{42} \cdot 5^{10} \)
$1.78718$
$(a+1), (-a-2), (2a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3, 5$
3B , 5B.4.1
$1$
\( 2 \cdot 3 \)
$1$
$0.318453365$
1.910720194
\( \frac{46969655}{32768} \)
\( \bigl[i + 1\) , \( -i + 1\) , \( i + 1\) , \( -353 i + 264\) , \( -1744 i + 317\bigr] \)
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-353i+264\right){x}-1744i+317$
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.