| 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-a2 |
1250.3-a |
$4$ |
$15$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1250.3 |
\( 2 \cdot 5^{4} \) |
\( 2^{10} \cdot 5^{16} \) |
$1.06266$ |
$(a+1), (-a-2), (2a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B.1.1, 5B.1.4 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.324496049$ |
$0.854500048$ |
1.109127558 |
\( -\frac{121945}{32} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -76\) , \( 298\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-76{x}+298$ |
| 1250.3-a3 |
1250.3-a |
$4$ |
$15$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1250.3 |
\( 2 \cdot 5^{4} \) |
\( 2^{2} \cdot 5^{8} \) |
$1.06266$ |
$(a+1), (-a-2), (2a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B.1.1, 5B.1.3 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.064899209$ |
$4.272500240$ |
1.109127558 |
\( -\frac{25}{2} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( 0\) , \( 2\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+2$ |
| 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-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 |
\( -\frac{349938025}{8} \) |
\( \bigl[i\) , \( -1\) , \( i\) , \( -3137\) , \( 68969\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}-3137{x}+68969$ |
| 1250.3-b2 |
1250.3-b |
$4$ |
$15$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1250.3 |
\( 2 \cdot 5^{4} \) |
\( 2^{10} \cdot 5^{4} \) |
$1.06266$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B, 5B.1.1 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$4.272500240$ |
1.709000096 |
\( -\frac{121945}{32} \) |
\( \bigl[i\) , \( -1\) , \( i\) , \( -2\) , \( -1\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}-2{x}-1$ |
| 1250.3-b3 |
1250.3-b |
$4$ |
$15$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1250.3 |
\( 2 \cdot 5^{4} \) |
\( 2^{2} \cdot 5^{20} \) |
$1.06266$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B, 5B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$0.854500048$ |
1.709000096 |
\( -\frac{25}{2} \) |
\( \bigl[i\) , \( -1\) , \( i\) , \( -12\) , \( 219\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}-12{x}+219$ |
| 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 |
\( \frac{46969655}{32768} \) |
\( \bigl[i\) , \( -1\) , \( i\) , \( 23\) , \( 9\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}+23{x}+9$ |
*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.
