| 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 |
| 92416.1-a1 |
92416.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
92416.1 |
\( 2^{8} \cdot 19^{2} \) |
\( 2^{12} \cdot 19^{2} \) |
$3.11606$ |
$(a+1), (19)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 1 \) |
$1.644458105$ |
$0.603483608$ |
1.984807025 |
\( -\frac{5698354821120}{19} a - \frac{4288599378432}{19} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1080 i + 1186\) , \( 11040 i + 22126\bigr] \) |
${y}^2={x}^{3}+\left(-1080i+1186\right){x}+11040i+22126$ |
| 92416.1-a2 |
92416.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
92416.1 |
\( 2^{8} \cdot 19^{2} \) |
\( 2^{12} \cdot 19^{2} \) |
$3.11606$ |
$(a+1), (19)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 1 \) |
$1.644458105$ |
$0.603483608$ |
1.984807025 |
\( \frac{5698354821120}{19} a - \frac{4288599378432}{19} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1080 i + 1186\) , \( 11040 i - 22126\bigr] \) |
${y}^2={x}^{3}+\left(1080i+1186\right){x}+11040i-22126$ |
| 92416.1-a3 |
92416.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
92416.1 |
\( 2^{8} \cdot 19^{2} \) |
\( 2^{12} \cdot 19^{10} \) |
$3.11606$ |
$(a+1), (19)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5Cs |
$1$ |
\( 5 \) |
$0.328891621$ |
$0.603483608$ |
1.984807025 |
\( -\frac{4741632}{2476099} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -14\) , \( 606\bigr] \) |
${y}^2={x}^{3}-14{x}+606$ |
| 92416.1-b1 |
92416.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
92416.1 |
\( 2^{8} \cdot 19^{2} \) |
\( 2^{12} \cdot 19^{2} \) |
$3.11606$ |
$(a+1), (19)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1.365713112$ |
$0.467654504$ |
5.109455107 |
\( -\frac{50357871050752}{19} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -3077\) , \( -64681\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-3077{x}-64681$ |
| 92416.1-b2 |
92416.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
92416.1 |
\( 2^{8} \cdot 19^{2} \) |
\( 2^{12} \cdot 19^{6} \) |
$3.11606$ |
$(a+1), (19)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Cs |
$1$ |
\( 2 \cdot 3 \) |
$0.151745901$ |
$1.402963512$ |
5.109455107 |
\( -\frac{89915392}{6859} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -37\) , \( -81\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-37{x}-81$ |
| 92416.1-b3 |
92416.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
92416.1 |
\( 2^{8} \cdot 19^{2} \) |
\( 2^{12} \cdot 19^{2} \) |
$3.11606$ |
$(a+1), (19)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.151745901$ |
$4.208890537$ |
5.109455107 |
\( \frac{32768}{19} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 3\) , \( -1\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+3{x}-1$ |
| 92416.1-c1 |
92416.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
92416.1 |
\( 2^{8} \cdot 19^{2} \) |
\( 2^{24} \cdot 19^{2} \) |
$3.11606$ |
$(a+1), (19)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.720811507$ |
$1.740066882$ |
5.017040932 |
\( \frac{283645}{19} a + \frac{733644}{19} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( -12 i + 28\) , \( -44 i - 32\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+\left(-12i+28\right){x}-44i-32$ |
| 92416.1-d1 |
92416.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
92416.1 |
\( 2^{8} \cdot 19^{2} \) |
\( 2^{30} \cdot 19^{2} \) |
$3.11606$ |
$(a+1), (19)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.472595983$ |
$0.852647549$ |
6.447324923 |
\( -\frac{413493625}{152} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( 248\) , \( 1424 i\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+248{x}+1424i$ |
| 92416.1-d2 |
92416.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
92416.1 |
\( 2^{8} \cdot 19^{2} \) |
\( 2^{78} \cdot 19^{2} \) |
$3.11606$ |
$(a+1), (19)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$4.253363854$ |
$0.094738616$ |
6.447324923 |
\( -\frac{69173457625}{2550136832} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( 1368\) , \( -157168 i\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+1368{x}-157168i$ |
| 92416.1-d3 |
92416.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
92416.1 |
\( 2^{8} \cdot 19^{2} \) |
\( 2^{42} \cdot 19^{6} \) |
$3.11606$ |
$(a+1), (19)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.472595983$ |
$0.284215849$ |
6.447324923 |
\( \frac{94196375}{3511808} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( -152\) , \( 5776 i\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}-152{x}+5776i$ |
| 92416.1-e1 |
92416.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
92416.1 |
\( 2^{8} \cdot 19^{2} \) |
\( 2^{22} \cdot 19^{2} \) |
$3.11606$ |
$(a+1), (19)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.177253355$ |
$2.303331491$ |
6.532371780 |
\( -\frac{31250}{19} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( 8\) , \( -16 i\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+8{x}-16i$ |
| 92416.1-f1 |
92416.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
92416.1 |
\( 2^{8} \cdot 19^{2} \) |
\( 2^{18} \cdot 19^{2} \) |
$3.11606$ |
$(a+1), (19)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.225942131$ |
$2.981887921$ |
5.389872907 |
\( \frac{27000}{19} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -5\) , \( -2 i\bigr] \) |
${y}^2={x}^{3}-5{x}-2i$ |
| 92416.1-g1 |
92416.1-g |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
92416.1 |
\( 2^{8} \cdot 19^{2} \) |
\( 2^{12} \cdot 19^{2} \) |
$3.11606$ |
$(a+1), (19)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 1 \) |
$0.595835310$ |
$4.183446943$ |
4.985290813 |
\( -\frac{13824}{19} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( -2\bigr] \) |
${y}^2={x}^{3}-2{x}-2$ |
| 92416.1-h1 |
92416.1-h |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
92416.1 |
\( 2^{8} \cdot 19^{2} \) |
\( 2^{16} \cdot 19^{2} \) |
$3.11606$ |
$(a+1), (19)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$2.415391886$ |
2.415391886 |
\( -\frac{4194304}{19} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( 21\) , \( 31 i\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+21{x}+31i$ |
| 92416.1-i1 |
92416.1-i |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
92416.1 |
\( 2^{8} \cdot 19^{2} \) |
\( 2^{16} \cdot 19^{2} \) |
$3.11606$ |
$(a+1), (19)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$3.397222379$ |
3.397222379 |
\( -\frac{1024}{19} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( 1\) , \( 3 i\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+{x}+3i$ |
| 92416.1-j1 |
92416.1-j |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
92416.1 |
\( 2^{8} \cdot 19^{2} \) |
\( 2^{24} \cdot 19^{2} \) |
$3.11606$ |
$(a+1), (19)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.720811507$ |
$1.740066882$ |
5.017040932 |
\( -\frac{283645}{19} a + \frac{733644}{19} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( 12 i + 28\) , \( -44 i + 32\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+\left(12i+28\right){x}-44i+32$ |
| 92416.1-k1 |
92416.1-k |
$2$ |
$5$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
92416.1 |
\( 2^{8} \cdot 19^{2} \) |
\( 2^{26} \cdot 19^{10} \) |
$3.11606$ |
$(a+1), (19)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$0.241263990$ |
4.825279813 |
\( -\frac{37966934881}{4952198} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( 1120\) , \( -15604 i\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+1120{x}-15604i$ |
| 92416.1-k2 |
92416.1-k |
$2$ |
$5$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
92416.1 |
\( 2^{8} \cdot 19^{2} \) |
\( 2^{34} \cdot 19^{2} \) |
$3.11606$ |
$(a+1), (19)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$1.206319953$ |
4.825279813 |
\( -\frac{1}{608} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( 0\) , \( -76 i\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}-76i$ |
*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.
