| 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 |
| 12544.1-a1 |
12544.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12544.1 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{16} \cdot 7^{2} \) |
$1.89137$ |
$(a+1), (7)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.186222298$ |
$4.016295718$ |
2.991695286 |
\( \frac{432}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 2 i\bigr] \) |
${y}^2={x}^{3}-{x}+2i$ |
| 12544.1-a2 |
12544.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12544.1 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{22} \cdot 7^{8} \) |
$1.89137$ |
$(a+1), (7)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.744889195$ |
$1.004073929$ |
2.991695286 |
\( \frac{11090466}{2401} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 59\) , \( -138 i\bigr] \) |
${y}^2={x}^{3}+59{x}-138i$ |
| 12544.1-a3 |
12544.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12544.1 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{4} \) |
$1.89137$ |
$(a+1), (7)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.744889195$ |
$2.008147859$ |
2.991695286 |
\( \frac{740772}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 19\) , \( 30 i\bigr] \) |
${y}^2={x}^{3}+19{x}+30i$ |
| 12544.1-a4 |
12544.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12544.1 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{22} \cdot 7^{2} \) |
$1.89137$ |
$(a+1), (7)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.979556781$ |
$1.004073929$ |
2.991695286 |
\( \frac{1443468546}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 299\) , \( 1990 i\bigr] \) |
${y}^2={x}^{3}+299{x}+1990i$ |
| 12544.1-b1 |
12544.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12544.1 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{14} \cdot 7^{2} \) |
$1.89137$ |
$(a+1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.321742177$ |
$4.250988810$ |
2.735444791 |
\( \frac{19872}{7} a + \frac{15296}{7} \) |
\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( -3\) , \( i + 1\bigr] \) |
${y}^2={x}^{3}+\left(-i+1\right){x}^{2}-3{x}+i+1$ |
| 12544.1-b2 |
12544.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12544.1 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{19} \cdot 7^{4} \) |
$1.89137$ |
$(a+1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.643484354$ |
$2.125494405$ |
2.735444791 |
\( -\frac{694948}{49} a + \frac{30148}{7} \) |
\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 10 i - 13\) , \( 31 i - 13\bigr] \) |
${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+\left(10i-13\right){x}+31i-13$ |
| 12544.1-c1 |
12544.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12544.1 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{14} \cdot 7^{2} \) |
$1.89137$ |
$(a+1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.321742177$ |
$4.250988810$ |
2.735444791 |
\( -\frac{19872}{7} a + \frac{15296}{7} \) |
\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( -3\) , \( i - 1\bigr] \) |
${y}^2={x}^{3}+\left(-i-1\right){x}^{2}-3{x}+i-1$ |
| 12544.1-c2 |
12544.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12544.1 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{19} \cdot 7^{4} \) |
$1.89137$ |
$(a+1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.643484354$ |
$2.125494405$ |
2.735444791 |
\( \frac{694948}{49} a + \frac{30148}{7} \) |
\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( -10 i - 13\) , \( 31 i + 13\bigr] \) |
${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+\left(-10i-13\right){x}+31i+13$ |
| 12544.1-d1 |
12544.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12544.1 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{2} \) |
$1.89137$ |
$(a+1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.612005445$ |
$4.990559254$ |
3.054249441 |
\( \frac{8000}{7} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( -2\) , \( 0\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}-2{x}$ |
| 12544.1-d2 |
12544.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12544.1 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{4} \) |
$1.89137$ |
$(a+1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.306002722$ |
$2.495279627$ |
3.054249441 |
\( \frac{125000}{49} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( 8\) , \( -8 i\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+8{x}-8i$ |
| 12544.1-e1 |
12544.1-e |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12544.1 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{60} \cdot 7^{2} \) |
$1.89137$ |
$(a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{2} \) |
$1$ |
$0.218854283$ |
1.969688554 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( 2728\) , \( 55920 i\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+2728{x}+55920i$ |
| 12544.1-e2 |
12544.1-e |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12544.1 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{28} \cdot 7^{2} \) |
$1.89137$ |
$(a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.969688554$ |
1.969688554 |
\( -\frac{15625}{28} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( 8\) , \( -16 i\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+8{x}-16i$ |
| 12544.1-e3 |
12544.1-e |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12544.1 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{36} \cdot 7^{6} \) |
$1.89137$ |
$(a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.656562851$ |
1.969688554 |
\( \frac{9938375}{21952} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( -72\) , \( 368 i\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}-72{x}+368i$ |
| 12544.1-e4 |
12544.1-e |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12544.1 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{30} \cdot 7^{12} \) |
$1.89137$ |
$(a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.328281425$ |
1.969688554 |
\( \frac{4956477625}{941192} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( 568\) , \( 4464 i\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+568{x}+4464i$ |
| 12544.1-e5 |
12544.1-e |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12544.1 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{26} \cdot 7^{4} \) |
$1.89137$ |
$(a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.984844277$ |
1.969688554 |
\( \frac{128787625}{98} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( 168\) , \( -784 i\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+168{x}-784i$ |
| 12544.1-e6 |
12544.1-e |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12544.1 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{42} \cdot 7^{4} \) |
$1.89137$ |
$(a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{3} \) |
$1$ |
$0.109427141$ |
1.969688554 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( 43688\) , \( 3529328 i\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+43688{x}+3529328i$ |
| 12544.1-f1 |
12544.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12544.1 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{2} \) |
$1.89137$ |
$(a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.197869643$ |
3.197869643 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( 0\) , \( -4 i\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}-4i$ |
| 12544.1-f2 |
12544.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12544.1 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{22} \cdot 7^{4} \) |
$1.89137$ |
$(a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.598934821$ |
3.197869643 |
\( \frac{3543122}{49} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( 40\) , \( -84 i\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+40{x}-84i$ |
*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.
