| 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 |
| 3375.6-a1 |
3375.6-a |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3375.6 |
\( 3^{3} \cdot 5^{3} \) |
\( 3^{13} \cdot 5^{11} \) |
$2.25893$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.726088001$ |
$0.837485832$ |
2.933528888 |
\( \frac{15729561967}{1476225} a - \frac{2695610401}{492075} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -34 a - 80\) , \( 256 a + 179\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-34a-80\right){x}+256a+179$ |
| 3375.6-a2 |
3375.6-a |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3375.6 |
\( 3^{3} \cdot 5^{3} \) |
\( 3^{8} \cdot 5^{10} \) |
$2.25893$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.452176003$ |
$1.674971665$ |
2.933528888 |
\( -\frac{1768663}{1215} a + \frac{880654}{405} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( a - 20\) , \( 12 a - 25\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a-20\right){x}+12a-25$ |
| 3375.6-b1 |
3375.6-b |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3375.6 |
\( 3^{3} \cdot 5^{3} \) |
\( 3^{10} \cdot 5^{10} \) |
$2.25893$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$2.513465836$ |
$1.182619820$ |
3.584939154 |
\( -\frac{84015547}{3375} a - \frac{4105442}{1125} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -7 a - 62\) , \( 33 a + 228\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-7a-62\right){x}+33a+228$ |
| 3375.6-b2 |
3375.6-b |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3375.6 |
\( 3^{3} \cdot 5^{3} \) |
\( 3^{10} \cdot 5^{10} \) |
$2.25893$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.837821945$ |
$1.182619820$ |
3.584939154 |
\( \frac{84015547}{3375} a - \frac{96331873}{3375} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -37 a + 48\) , \( 24 a - 184\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-37a+48\right){x}+24a-184$ |
| 3375.6-b3 |
3375.6-b |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3375.6 |
\( 3^{3} \cdot 5^{3} \) |
\( 3^{14} \cdot 5^{14} \) |
$2.25893$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{6} \) |
$1.256732918$ |
$0.591309910$ |
3.584939154 |
\( -\frac{1217478647}{11390625} a + \frac{227748383}{3796875} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 33 a - 47\) , \( 254 a + 339\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(33a-47\right){x}+254a+339$ |
| 3375.6-b4 |
3375.6-b |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3375.6 |
\( 3^{3} \cdot 5^{3} \) |
\( 3^{14} \cdot 5^{14} \) |
$2.25893$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{6} \cdot 3 \) |
$0.418910972$ |
$0.591309910$ |
3.584939154 |
\( \frac{1217478647}{11390625} a - \frac{534233498}{11390625} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 3 a + 63\) , \( 265 a - 628\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(3a+63\right){x}+265a-628$ |
| 3375.6-b5 |
3375.6-b |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3375.6 |
\( 3^{3} \cdot 5^{3} \) |
\( 3^{13} \cdot 5^{19} \) |
$2.25893$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{6} \cdot 3 \) |
$0.209455486$ |
$0.295654955$ |
3.584939154 |
\( -\frac{93926997067673}{19775390625} a + \frac{66606305361919}{6591796875} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 268 a - 822\) , \( 3819 a - 7339\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(268a-822\right){x}+3819a-7339$ |
| 3375.6-b6 |
3375.6-b |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3375.6 |
\( 3^{3} \cdot 5^{3} \) |
\( 3^{13} \cdot 5^{19} \) |
$2.25893$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$2.513465836$ |
$0.295654955$ |
3.584939154 |
\( \frac{93926997067673}{19775390625} a + \frac{105891919018084}{19775390625} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -192 a + 853\) , \( 4484 a + 1644\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-192a+853\right){x}+4484a+1644$ |
| 3375.6-b7 |
3375.6-b |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3375.6 |
\( 3^{3} \cdot 5^{3} \) |
\( 3^{19} \cdot 5^{13} \) |
$2.25893$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.837821945$ |
$0.295654955$ |
3.584939154 |
\( -\frac{59052841710247}{332150625} a + \frac{72460071479059}{332150625} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 378 a + 1188\) , \( 11515 a - 19753\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(378a+1188\right){x}+11515a-19753$ |
| 3375.6-b8 |
3375.6-b |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3375.6 |
\( 3^{3} \cdot 5^{3} \) |
\( 3^{19} \cdot 5^{13} \) |
$2.25893$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{6} \) |
$0.628366459$ |
$0.295654955$ |
3.584939154 |
\( \frac{59052841710247}{332150625} a + \frac{4469076589604}{110716875} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 898 a - 707\) , \( 11348 a + 6018\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(898a-707\right){x}+11348a+6018$ |
| 3375.6-c1 |
3375.6-c |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3375.6 |
\( 3^{3} \cdot 5^{3} \) |
\( 3^{13} \cdot 5^{5} \) |
$2.25893$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 5 \) |
$0.095926906$ |
$1.872675252$ |
4.333078472 |
\( \frac{15729561967}{1476225} a - \frac{2695610401}{492075} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 10 a - 17\) , \( -34 a - 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(10a-17\right){x}-34a-3$ |
| 3375.6-c2 |
3375.6-c |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3375.6 |
\( 3^{3} \cdot 5^{3} \) |
\( 3^{8} \cdot 5^{4} \) |
$2.25893$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.191853812$ |
$3.745350504$ |
4.333078472 |
\( -\frac{1768663}{1215} a + \frac{880654}{405} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -2\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}-2{x}-a$ |
| 3375.6-d1 |
3375.6-d |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3375.6 |
\( 3^{3} \cdot 5^{3} \) |
\( 3^{11} \cdot 5^{16} \) |
$2.25893$ |
$(-a), (a-1), (-a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.422896913$ |
4.080262942 |
\( -\frac{3412573008482}{31640625} a - \frac{1003065641677}{10546875} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 280 a + 385\) , \( 2185 a - 7730\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(280a+385\right){x}+2185a-7730$ |
| 3375.6-d2 |
3375.6-d |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3375.6 |
\( 3^{3} \cdot 5^{3} \) |
\( 3^{11} \cdot 5^{16} \) |
$2.25893$ |
$(-a), (a-1), (-a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.422896913$ |
4.080262942 |
\( \frac{3412573008482}{31640625} a - \frac{6421769933513}{31640625} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 420 a - 125\) , \( 2449 a + 4294\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(420a-125\right){x}+2449a+4294$ |
| 3375.6-d3 |
3375.6-d |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3375.6 |
\( 3^{3} \cdot 5^{3} \) |
\( 3^{10} \cdot 5^{14} \) |
$2.25893$ |
$(-a), (a-1), (-a-1), (a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.845793826$ |
4.080262942 |
\( \frac{5929741}{5625} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 30 a + 10\) , \( 85 a - 80\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(30a+10\right){x}+85a-80$ |
| 3375.6-d4 |
3375.6-d |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3375.6 |
\( 3^{3} \cdot 5^{3} \) |
\( 3^{8} \cdot 5^{10} \) |
$2.25893$ |
$(-a), (a-1), (-a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.691587653$ |
4.080262942 |
\( \frac{205379}{75} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -10 a - 5\) , \( 9 a + 4\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-10a-5\right){x}+9a+4$ |
*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.
