| 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 |
| 20808.5-a1 |
20808.5-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20808.5 |
\( 2^{3} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{10} \cdot 3^{8} \cdot 17^{3} \) |
$3.03558$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.638672685$ |
1.158716568 |
\( -\frac{216259784}{70227} a - \frac{740698438}{70227} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 16 a + 15\) , \( 59\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(16a+15\right){x}+59$ |
| 20808.5-a2 |
20808.5-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20808.5 |
\( 2^{3} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{11} \cdot 3^{16} \cdot 17^{3} \) |
$3.03558$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.819336342$ |
1.158716568 |
\( -\frac{6773137523}{17065161} a - \frac{14265581908}{17065161} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -14 a + 55\) , \( 142 a + 187\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-14a+55\right){x}+142a+187$ |
| 20808.5-b1 |
20808.5-b |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20808.5 |
\( 2^{3} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 17^{10} \) |
$3.03558$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$0.595188230$ |
0.841723267 |
\( \frac{57530252288}{38336139} \) |
\( \bigl[0\) , \( -1\) , \( a\) , \( 128\) , \( 174\bigr] \) |
${y}^2+a{y}={x}^{3}-{x}^{2}+128{x}+174$ |
| 20808.5-c1 |
20808.5-c |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20808.5 |
\( 2^{3} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{10} \cdot 3^{8} \cdot 17^{3} \) |
$3.03558$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.638672685$ |
1.158716568 |
\( \frac{216259784}{70227} a - \frac{740698438}{70227} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -16 a + 15\) , \( 59\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-16a+15\right){x}+59$ |
| 20808.5-c2 |
20808.5-c |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20808.5 |
\( 2^{3} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{11} \cdot 3^{16} \cdot 17^{3} \) |
$3.03558$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.819336342$ |
1.158716568 |
\( \frac{6773137523}{17065161} a - \frac{14265581908}{17065161} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 14 a + 55\) , \( -142 a + 187\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(14a+55\right){x}-142a+187$ |
| 20808.5-d1 |
20808.5-d |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20808.5 |
\( 2^{3} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{4} \cdot 3^{14} \cdot 17^{8} \) |
$3.03558$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 5 \cdot 13 \) |
$0.066462902$ |
$0.401746248$ |
4.908959850 |
\( -\frac{13596667005814784}{2263710671811} a + \frac{35649488015527936}{2263710671811} \) |
\( \bigl[0\) , \( a\) , \( a\) , \( -103 a + 468\) , \( -2360 a - 1770\bigr] \) |
${y}^2+a{y}={x}^{3}+a{x}^{2}+\left(-103a+468\right){x}-2360a-1770$ |
| 20808.5-e1 |
20808.5-e |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20808.5 |
\( 2^{3} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{4} \cdot 3^{14} \cdot 17^{8} \) |
$3.03558$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 5 \cdot 13 \) |
$0.066462902$ |
$0.401746248$ |
4.908959850 |
\( \frac{13596667005814784}{2263710671811} a + \frac{35649488015527936}{2263710671811} \) |
\( \bigl[0\) , \( -a\) , \( a\) , \( 103 a + 468\) , \( 2360 a - 1770\bigr] \) |
${y}^2+a{y}={x}^{3}-a{x}^{2}+\left(103a+468\right){x}+2360a-1770$ |
| 20808.5-f1 |
20808.5-f |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20808.5 |
\( 2^{3} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{10} \cdot 3^{8} \cdot 17^{4} \) |
$3.03558$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$0.418645842$ |
$1.473245113$ |
6.977932709 |
\( -\frac{31250}{23409} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -2\) , \( 42\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-2{x}+42$ |
| 20808.5-f2 |
20808.5-f |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20808.5 |
\( 2^{3} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{11} \cdot 3^{10} \cdot 17^{5} \) |
$3.03558$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.837291685$ |
$0.736622556$ |
6.977932709 |
\( -\frac{5476739736875}{547981281} a + \frac{23093460929000}{547981281} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -110 a + 78\) , \( -40 a + 850\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-110a+78\right){x}-40a+850$ |
| 20808.5-f3 |
20808.5-f |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20808.5 |
\( 2^{3} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{11} \cdot 3^{10} \cdot 17^{5} \) |
$3.03558$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.837291685$ |
$0.736622556$ |
6.977932709 |
\( \frac{5476739736875}{547981281} a + \frac{23093460929000}{547981281} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 110 a + 78\) , \( 40 a + 850\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(110a+78\right){x}+40a+850$ |
| 20808.5-f4 |
20808.5-f |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20808.5 |
\( 2^{3} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 17^{2} \) |
$3.03558$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.837291685$ |
$2.946490226$ |
6.977932709 |
\( \frac{12194500}{153} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -12\) , \( 18\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-12{x}+18$ |
| 20808.5-g1 |
20808.5-g |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20808.5 |
\( 2^{3} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{4} \cdot 3^{10} \cdot 17^{2} \) |
$3.03558$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2 \cdot 5^{2} \) |
$0.035837594$ |
$2.721420930$ |
6.896354363 |
\( -\frac{2249728}{4131} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( -4\) , \( -8\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}-4{x}-8$ |
| 20808.5-h1 |
20808.5-h |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20808.5 |
\( 2^{3} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{10} \cdot 3^{4} \cdot 17^{8} \) |
$3.03558$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.809400023$ |
4.578657960 |
\( \frac{1285471294}{751689} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 72\) , \( -36\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+72{x}-36$ |
| 20808.5-h2 |
20808.5-h |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20808.5 |
\( 2^{3} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 17^{4} \) |
$3.03558$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$1$ |
$1.618800046$ |
4.578657960 |
\( \frac{40873252}{23409} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -18\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-18{x}$ |
| 20808.5-h3 |
20808.5-h |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20808.5 |
\( 2^{3} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{10} \cdot 3^{16} \cdot 17^{2} \) |
$3.03558$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1$ |
$0.809400023$ |
4.578657960 |
\( \frac{22994537186}{111537} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -188\) , \( 1020\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-188{x}+1020$ |
| 20808.5-h4 |
20808.5-h |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20808.5 |
\( 2^{3} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{11} \cdot 3^{2} \cdot 17^{10} \) |
$3.03558$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.404700011$ |
4.578657960 |
\( -\frac{1400716334131201}{20927272323} a + \frac{1883759902489320}{6975757441} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -30 a + 792\) , \( -6036 a - 828\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-30a+792\right){x}-6036a-828$ |
| 20808.5-h5 |
20808.5-h |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20808.5 |
\( 2^{3} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{11} \cdot 3^{2} \cdot 17^{10} \) |
$3.03558$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.404700011$ |
4.578657960 |
\( \frac{1400716334131201}{20927272323} a + \frac{1883759902489320}{6975757441} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 30 a + 792\) , \( 6036 a - 828\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(30a+792\right){x}+6036a-828$ |
| 20808.5-h6 |
20808.5-h |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20808.5 |
\( 2^{3} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 17^{2} \) |
$3.03558$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$3.237600092$ |
4.578657960 |
\( \frac{61918288}{153} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -13\) , \( -16\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-13{x}-16$ |
*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.
