| 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 |
| 54756.2-a1 |
54756.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
54756.2 |
\( 2^{2} \cdot 3^{4} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{18} \cdot 13^{8} \) |
$2.73386$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.248269512$ |
0.496539025 |
\( -\frac{1213857792}{28561} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1512\) , \( -23085\bigr] \) |
${y}^2={x}^{3}-1512{x}-23085$ |
| 54756.2-a2 |
54756.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
54756.2 |
\( 2^{2} \cdot 3^{4} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{18} \cdot 13^{4} \) |
$2.73386$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.248269512$ |
0.496539025 |
\( \frac{315978926832}{169} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 6081\) , \( -179513 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+6081{x}-179513i$ |
| 54756.2-b1 |
54756.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
54756.2 |
\( 2^{2} \cdot 3^{4} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 13^{4} \) |
$2.73386$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.256255218$ |
$1.579540092$ |
4.857184697 |
\( \frac{432}{169} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i - 3\) , \( 32 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-i-3\right){x}+32i$ |
| 54756.2-b2 |
54756.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
54756.2 |
\( 2^{2} \cdot 3^{4} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 13^{2} \) |
$2.73386$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.256255218$ |
$1.579540092$ |
4.857184697 |
\( \frac{442368}{13} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -36\) , \( 81\bigr] \) |
${y}^2={x}^{3}-36{x}+81$ |
| 54756.2-b3 |
54756.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
54756.2 |
\( 2^{2} \cdot 3^{4} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 13^{5} \) |
$2.73386$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.256255218$ |
$0.789770046$ |
4.857184697 |
\( -\frac{793539828}{28561} a + \frac{1773275112}{28561} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -136 i - 93\) , \( 743 i + 162\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-136i-93\right){x}+743i+162$ |
| 54756.2-b4 |
54756.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
54756.2 |
\( 2^{2} \cdot 3^{4} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 13^{5} \) |
$2.73386$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.256255218$ |
$0.789770046$ |
4.857184697 |
\( \frac{793539828}{28561} a + \frac{1773275112}{28561} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( 134 i - 93\) , \( 743 i - 162\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(134i-93\right){x}+743i-162$ |
| 54756.2-c1 |
54756.2-c |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
54756.2 |
\( 2^{2} \cdot 3^{4} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{24} \cdot 13^{2} \) |
$2.73386$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 2^{2} \) |
$1$ |
$0.627651774$ |
2.510607098 |
\( \frac{16384000}{9477} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -120\) , \( -11\bigr] \) |
${y}^2={x}^{3}-120{x}-11$ |
| 54756.2-c2 |
54756.2-c |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
54756.2 |
\( 2^{2} \cdot 3^{4} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{14} \cdot 13^{12} \) |
$2.73386$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{3} \) |
$1$ |
$0.209217258$ |
2.510607098 |
\( \frac{181037698000}{14480427} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i + 1683\) , \( 25528 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-i+1683\right){x}+25528i$ |
| 54756.2-c3 |
54756.2-c |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
54756.2 |
\( 2^{2} \cdot 3^{4} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{18} \cdot 13^{4} \) |
$2.73386$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$1$ |
$0.627651774$ |
2.510607098 |
\( \frac{1409938000}{4563} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i + 333\) , \( -2174 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-i+333\right){x}-2174i$ |
| 54756.2-c4 |
54756.2-c |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
54756.2 |
\( 2^{2} \cdot 3^{4} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{16} \cdot 13^{6} \) |
$2.73386$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2^{2} \cdot 3^{3} \) |
$1$ |
$0.209217258$ |
2.510607098 |
\( \frac{2725888000000}{19773} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -6600\) , \( 206377\bigr] \) |
${y}^2={x}^{3}-6600{x}+206377$ |
| 54756.2-d1 |
54756.2-d |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
54756.2 |
\( 2^{2} \cdot 3^{4} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 13^{8} \) |
$2.73386$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.744808538$ |
4.468851233 |
\( -\frac{1213857792}{28561} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -168\) , \( -855\bigr] \) |
${y}^2={x}^{3}-168{x}-855$ |
| 54756.2-d2 |
54756.2-d |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
54756.2 |
\( 2^{2} \cdot 3^{4} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 13^{4} \) |
$2.73386$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.744808538$ |
4.468851233 |
\( \frac{315978926832}{169} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i + 675\) , \( -6424 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-i+675\right){x}-6424i$ |
| 54756.2-e1 |
54756.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
54756.2 |
\( 2^{2} \cdot 3^{4} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{14} \cdot 13^{4} \) |
$2.73386$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.196723962$ |
4.786895849 |
\( \frac{3631696}{507} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i + 45\) , \( 126 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-i+45\right){x}+126i$ |
| 54756.2-e2 |
54756.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
54756.2 |
\( 2^{2} \cdot 3^{4} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{16} \cdot 13^{2} \) |
$2.73386$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.196723962$ |
4.786895849 |
\( \frac{1048576}{117} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -48\) , \( -115\bigr] \) |
${y}^2={x}^{3}-48{x}-115$ |
*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.
