| 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 |
| 12675.2-a1 |
12675.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12675.2 |
\( 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{14} \cdot 5^{2} \cdot 13^{6} \) |
$1.64224$ |
$(-2a+1), (-4a+1), (4a-3), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$0.680358928$ |
1.571221642 |
\( -\frac{762549907456}{24024195} \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( -190 a + 190\) , \( 1101\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(-190a+190\right){x}+1101$ |
| 12675.2-b1 |
12675.2-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12675.2 |
\( 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{2} \cdot 5^{32} \cdot 13^{2} \) |
$1.64224$ |
$(-2a+1), (-4a+1), (4a-3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1.386213803$ |
$0.092658541$ |
2.373039851 |
\( -\frac{55150149867714721}{5950927734375} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -7930 a + 7930\) , \( -296725\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-7930a+7930\right){x}-296725$ |
| 12675.2-b2 |
12675.2-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12675.2 |
\( 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 5^{4} \cdot 13^{16} \) |
$1.64224$ |
$(-2a+1), (-4a+1), (4a-3), (5)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{9} \) |
$0.693106901$ |
$0.185317083$ |
2.373039851 |
\( \frac{24487529386319}{183539412225} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 605 a - 605\) , \( -19750\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(605a-605\right){x}-19750$ |
| 12675.2-b3 |
12675.2-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12675.2 |
\( 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{32} \cdot 5^{2} \cdot 13^{2} \) |
$1.64224$ |
$(-2a+1), (-4a+1), (4a-3), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1.386213803$ |
$0.370634167$ |
2.373039851 |
\( \frac{1023887723039}{2798036865} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 210 a - 210\) , \( 2277\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(210a-210\right){x}+2277$ |
| 12675.2-b4 |
12675.2-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12675.2 |
\( 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{16} \cdot 5^{4} \cdot 13^{4} \) |
$1.64224$ |
$(-2a+1), (-4a+1), (4a-3), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$0.693106901$ |
$0.741268334$ |
2.373039851 |
\( \frac{168288035761}{27720225} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -115 a + 115\) , \( 392\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-115a+115\right){x}+392$ |
| 12675.2-b5 |
12675.2-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12675.2 |
\( 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{8} \cdot 5^{8} \cdot 13^{8} \) |
$1.64224$ |
$(-2a+1), (-4a+1), (4a-3), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{9} \) |
$0.346553450$ |
$0.370634167$ |
2.373039851 |
\( \frac{15551989015681}{1445900625} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -520 a + 520\) , \( -4225\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-520a+520\right){x}-4225$ |
| 12675.2-b6 |
12675.2-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12675.2 |
\( 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{8} \cdot 5^{2} \cdot 13^{2} \) |
$1.64224$ |
$(-2a+1), (-4a+1), (4a-3), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.386213803$ |
$1.482536669$ |
2.373039851 |
\( \frac{147281603041}{5265} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -110 a + 110\) , \( 435\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-110a+110\right){x}+435$ |
| 12675.2-b7 |
12675.2-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12675.2 |
\( 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 5^{16} \cdot 13^{4} \) |
$1.64224$ |
$(-2a+1), (-4a+1), (4a-3), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$0.693106901$ |
$0.185317083$ |
2.373039851 |
\( \frac{59319456301170001}{594140625} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -8125 a + 8125\) , \( -282568\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-8125a+8125\right){x}-282568$ |
| 12675.2-b8 |
12675.2-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12675.2 |
\( 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{2} \cdot 5^{8} \cdot 13^{2} \) |
$1.64224$ |
$(-2a+1), (-4a+1), (4a-3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1.386213803$ |
$0.092658541$ |
2.373039851 |
\( \frac{242970740812818720001}{24375} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -130000 a + 130000\) , \( -18051943\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-130000a+130000\right){x}-18051943$ |
| 12675.2-c1 |
12675.2-c |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12675.2 |
\( 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
$1.64224$ |
$(-2a+1), (-4a+1), (4a-3), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.099517256$ |
$5.819237497$ |
2.674815524 |
\( -\frac{4096}{195} \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 0\) , \( -1\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}-1$ |
| 12675.2-d1 |
12675.2-d |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12675.2 |
\( 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{6} \cdot 5^{14} \cdot 13^{2} \) |
$1.64224$ |
$(-2a+1), (-4a+1), (4a-3), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2 \cdot 3 \cdot 7 \) |
$0.037671158$ |
$0.779030811$ |
2.846507032 |
\( -\frac{32278933504}{27421875} \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 66 a\) , \( -349\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+66a{x}-349$ |
*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.
