| 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 |
| 8712.5-a1 |
8712.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
8712.5 |
\( 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{3} \cdot 11^{3} \) |
$2.44182$ |
$(a), (-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.297396174$ |
$3.022538076$ |
2.772869275 |
\( -\frac{179393408}{1089} a - \frac{580479536}{1089} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 11 a - 3\) , \( 17 a + 11\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(11a-3\right){x}+17a+11$ |
| 8712.5-a2 |
8712.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
8712.5 |
\( 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{10} \cdot 3^{3} \cdot 11^{9} \) |
$2.44182$ |
$(a), (-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1.297396174$ |
$0.755634519$ |
2.772869275 |
\( \frac{88067362666004}{1929229929} a - \frac{120881007905362}{1929229929} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 71 a - 158\) , \( -512 a + 635\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(71a-158\right){x}-512a+635$ |
| 8712.5-a3 |
8712.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
8712.5 |
\( 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 11^{6} \) |
$2.44182$ |
$(a), (-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$0.648698087$ |
$1.511269038$ |
2.772869275 |
\( -\frac{403671568}{1185921} a + \frac{1088349572}{1185921} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 11 a - 8\) , \( 10 a + 23\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(11a-8\right){x}+10a+23$ |
| 8712.5-a4 |
8712.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
8712.5 |
\( 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{10} \cdot 3^{12} \cdot 11^{6} \) |
$2.44182$ |
$(a), (-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.297396174$ |
$0.755634519$ |
2.772869275 |
\( \frac{78368259788}{96059601} a + \frac{251208234482}{96059601} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -49 a + 62\) , \( 84 a + 219\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-49a+62\right){x}+84a+219$ |
| 8712.5-a5 |
8712.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
8712.5 |
\( 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{11} \cdot 3^{24} \cdot 11^{3} \) |
$2.44182$ |
$(a), (-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.594792348$ |
$0.377817259$ |
2.772869275 |
\( -\frac{71786530937251}{5208653241} a + \frac{104672303006342}{5208653241} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -379 a + 282\) , \( 260 a - 5545\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-379a+282\right){x}+260a-5545$ |
| 8712.5-a6 |
8712.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
8712.5 |
\( 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{11} \cdot 3^{6} \cdot 11^{9} \) |
$2.44182$ |
$(a), (-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.594792348$ |
$0.377817259$ |
2.772869275 |
\( \frac{53255432145300427}{17363069361} a + \frac{30514169882939386}{17363069361} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -679 a + 962\) , \( 5124 a + 17967\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-679a+962\right){x}+5124a+17967$ |
| 8712.5-b1 |
8712.5-b |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
8712.5 |
\( 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{3} \cdot 11^{3} \) |
$2.44182$ |
$(a), (-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.297396174$ |
$3.022538076$ |
2.772869275 |
\( \frac{179393408}{1089} a - \frac{580479536}{1089} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -11 a - 3\) , \( -17 a + 11\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-11a-3\right){x}-17a+11$ |
| 8712.5-b2 |
8712.5-b |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
8712.5 |
\( 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{10} \cdot 3^{3} \cdot 11^{9} \) |
$2.44182$ |
$(a), (-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1.297396174$ |
$0.755634519$ |
2.772869275 |
\( -\frac{88067362666004}{1929229929} a - \frac{120881007905362}{1929229929} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -71 a - 158\) , \( 512 a + 635\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-71a-158\right){x}+512a+635$ |
| 8712.5-b3 |
8712.5-b |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
8712.5 |
\( 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 11^{6} \) |
$2.44182$ |
$(a), (-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$0.648698087$ |
$1.511269038$ |
2.772869275 |
\( \frac{403671568}{1185921} a + \frac{1088349572}{1185921} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -11 a - 8\) , \( -10 a + 23\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-11a-8\right){x}-10a+23$ |
| 8712.5-b4 |
8712.5-b |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
8712.5 |
\( 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{10} \cdot 3^{12} \cdot 11^{6} \) |
$2.44182$ |
$(a), (-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.297396174$ |
$0.755634519$ |
2.772869275 |
\( -\frac{78368259788}{96059601} a + \frac{251208234482}{96059601} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 49 a + 62\) , \( -84 a + 219\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(49a+62\right){x}-84a+219$ |
| 8712.5-b5 |
8712.5-b |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
8712.5 |
\( 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{11} \cdot 3^{24} \cdot 11^{3} \) |
$2.44182$ |
$(a), (-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.594792348$ |
$0.377817259$ |
2.772869275 |
\( \frac{71786530937251}{5208653241} a + \frac{104672303006342}{5208653241} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 379 a + 282\) , \( -260 a - 5545\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(379a+282\right){x}-260a-5545$ |
| 8712.5-b6 |
8712.5-b |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
8712.5 |
\( 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{11} \cdot 3^{6} \cdot 11^{9} \) |
$2.44182$ |
$(a), (-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.594792348$ |
$0.377817259$ |
2.772869275 |
\( -\frac{53255432145300427}{17363069361} a + \frac{30514169882939386}{17363069361} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 679 a + 962\) , \( -5124 a + 17967\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(679a+962\right){x}-5124a+17967$ |
| 8712.5-c1 |
8712.5-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
8712.5 |
\( 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{10} \cdot 3^{2} \cdot 11^{8} \) |
$2.44182$ |
$(a), (-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.823221395$ |
$1.307767102$ |
3.045033333 |
\( \frac{36382894}{43923} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 23\) , \( -37\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+23{x}-37$ |
| 8712.5-c2 |
8712.5-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
8712.5 |
\( 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 11^{4} \) |
$2.44182$ |
$(a), (-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.411610697$ |
$2.615534204$ |
3.045033333 |
\( \frac{3650692}{1089} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -7\) , \( -7\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-7{x}-7$ |
| 8712.5-c3 |
8712.5-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
8712.5 |
\( 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 11^{2} \) |
$2.44182$ |
$(a), (-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.823221395$ |
$5.231068409$ |
3.045033333 |
\( \frac{810448}{33} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -2\) , \( 2\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-2{x}+2$ |
| 8712.5-c4 |
8712.5-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
8712.5 |
\( 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{10} \cdot 3^{8} \cdot 11^{2} \) |
$2.44182$ |
$(a), (-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.823221395$ |
$1.307767102$ |
3.045033333 |
\( \frac{5690357426}{891} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -117\) , \( -513\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-117{x}-513$ |
| 8712.5-d1 |
8712.5-d |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
8712.5 |
\( 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 11^{4} \) |
$2.44182$ |
$(a), (-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.163842054$ |
$2.779523261$ |
3.864220914 |
\( \frac{85555616}{3267} a - \frac{97997776}{3267} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 7 a + 5\) , \( 9\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(7a+5\right){x}+9$ |
| 8712.5-d2 |
8712.5-d |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
8712.5 |
\( 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 11^{2} \) |
$2.44182$ |
$(a), (-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.081921027$ |
$2.779523261$ |
3.864220914 |
\( -\frac{5261312}{8019} a + \frac{6842368}{8019} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 2 a + 4\) , \( -2 a - 1\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(2a+4\right){x}-2a-1$ |
| 8712.5-e1 |
8712.5-e |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
8712.5 |
\( 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 11^{4} \) |
$2.44182$ |
$(a), (-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.163842054$ |
$2.779523261$ |
3.864220914 |
\( -\frac{85555616}{3267} a - \frac{97997776}{3267} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -7 a + 5\) , \( 9\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-7a+5\right){x}+9$ |
| 8712.5-e2 |
8712.5-e |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
8712.5 |
\( 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 11^{2} \) |
$2.44182$ |
$(a), (-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.081921027$ |
$2.779523261$ |
3.864220914 |
\( \frac{5261312}{8019} a + \frac{6842368}{8019} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -2 a + 4\) , \( 2 a - 1\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-2a+4\right){x}+2a-1$ |
| 8712.5-f1 |
8712.5-f |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
8712.5 |
\( 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{10} \cdot 3^{28} \cdot 11^{4} \) |
$2.44182$ |
$(a), (-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \cdot 7^{2} \) |
$0.178239312$ |
$0.218400464$ |
5.395083000 |
\( -\frac{27403349188178}{578739249} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -1994\) , \( 35226\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-1994{x}+35226$ |
| 8712.5-f2 |
8712.5-f |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
8712.5 |
\( 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{11} \cdot 3^{35} \cdot 11^{5} \) |
$2.44182$ |
$(a), (-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 7^{2} \) |
$0.356478625$ |
$0.109200232$ |
5.395083000 |
\( -\frac{141442261473535202245}{334939118333084001} a + \frac{102413516146441233896}{334939118333084001} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 1550 a - 1914\) , \( 55576 a + 46786\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(1550a-1914\right){x}+55576a+46786$ |
| 8712.5-f3 |
8712.5-f |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
8712.5 |
\( 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{11} \cdot 3^{35} \cdot 11^{5} \) |
$2.44182$ |
$(a), (-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 7^{2} \) |
$0.356478625$ |
$0.109200232$ |
5.395083000 |
\( \frac{141442261473535202245}{334939118333084001} a + \frac{102413516146441233896}{334939118333084001} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -1550 a - 1914\) , \( -55576 a + 46786\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-1550a-1914\right){x}-55576a+46786$ |
| 8712.5-f4 |
8712.5-f |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
8712.5 |
\( 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{14} \cdot 11^{2} \) |
$2.44182$ |
$(a), (-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 7^{2} \) |
$0.356478625$ |
$0.436800929$ |
5.395083000 |
\( \frac{55635379958596}{24057} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -2004\) , \( 34866\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-2004{x}+34866$ |
| 8712.5-g1 |
8712.5-g |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
8712.5 |
\( 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 11^{2} \) |
$2.44182$ |
$(a), (-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.338500232$ |
$2.850951843$ |
5.459135104 |
\( \frac{2048}{891} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 1\) , \( 6\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+{x}+6$ |
| 8712.5-g2 |
8712.5-g |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
8712.5 |
\( 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 11^{8} \) |
$2.44182$ |
$(a), (-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.354000931$ |
$1.425475921$ |
5.459135104 |
\( \frac{122657188}{43923} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -26\) , \( 36\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-26{x}+36$ |
| 8712.5-g3 |
8712.5-g |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
8712.5 |
\( 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 11^{4} \) |
$2.44182$ |
$(a), (-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.677000465$ |
$2.850951843$ |
5.459135104 |
\( \frac{37642192}{1089} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -11\) , \( -12\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-11{x}-12$ |
| 8712.5-g4 |
8712.5-g |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
8712.5 |
\( 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 11^{2} \) |
$2.44182$ |
$(a), (-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1.354000931$ |
$1.425475921$ |
5.459135104 |
\( \frac{37736227588}{33} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -176\) , \( -870\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-176{x}-870$ |
| 8712.5-h1 |
8712.5-h |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
8712.5 |
\( 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{10} \cdot 3^{4} \cdot 11^{4} \) |
$2.44182$ |
$(a), (-a-1), (a-1), (a+3), (a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$2.408219204$ |
3.405736260 |
\( \frac{1714750}{1089} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 8\) , \( -4\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+8{x}-4$ |
| 8712.5-h2 |
8712.5-h |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
8712.5 |
\( 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 11^{2} \) |
$2.44182$ |
$(a), (-a-1), (a-1), (a+3), (a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.816438409$ |
3.405736260 |
\( \frac{62500}{33} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -2\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-2{x}$ |
| 8712.5-h3 |
8712.5-h |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
8712.5 |
\( 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{11} \cdot 3^{5} \cdot 11^{5} \) |
$2.44182$ |
$(a), (-a-1), (a-1), (a+3), (a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.204109602$ |
3.405736260 |
\( -\frac{195051546625}{1185921} a + \frac{175802465000}{1185921} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -10 a + 88\) , \( -220 a - 92\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-10a+88\right){x}-220a-92$ |
| 8712.5-h4 |
8712.5-h |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
8712.5 |
\( 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{11} \cdot 3^{5} \cdot 11^{5} \) |
$2.44182$ |
$(a), (-a-1), (a-1), (a+3), (a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.204109602$ |
3.405736260 |
\( \frac{195051546625}{1185921} a + \frac{175802465000}{1185921} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 10 a + 88\) , \( 220 a - 92\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(10a+88\right){x}+220a-92$ |
*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.
