| 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 |
| 720.1-a1 |
720.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{16} \cdot 3^{2} \cdot 5^{2} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.891621139$ |
$6.963173771$ |
1.963304175 |
\( \frac{21296}{15} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 4\) , \( 0\bigr] \) |
${y}^2={x}^3-{x}^2+4{x}$ |
| 720.1-a2 |
720.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{20} \cdot 3^{4} \cdot 5^{4} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$0.445810569$ |
$3.481586885$ |
1.963304175 |
\( \frac{470596}{225} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -16\) , \( 16\bigr] \) |
${y}^2={x}^3-{x}^2-16{x}+16$ |
| 720.1-a3 |
720.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{22} \cdot 3^{2} \cdot 5^{8} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.891621139$ |
$1.740793442$ |
1.963304175 |
\( \frac{136835858}{1875} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -136\) , \( -560\bigr] \) |
${y}^2={x}^3-{x}^2-136{x}-560$ |
| 720.1-a4 |
720.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{22} \cdot 3^{8} \cdot 5^{2} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.222905284$ |
$1.740793442$ |
1.963304175 |
\( \frac{546718898}{405} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -216\) , \( 1296\bigr] \) |
${y}^2={x}^3-{x}^2-216{x}+1296$ |
| 720.1-b1 |
720.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{10} \cdot 3^{2} \cdot 5^{16} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$4.584915408$ |
$0.765787510$ |
4.441192498 |
\( -\frac{27995042}{1171875} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -13\) , \( -278\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-13{x}-278$ |
| 720.1-b2 |
720.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{8} \cdot 3^{16} \cdot 5^{2} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$2.292457704$ |
$1.531575020$ |
4.441192498 |
\( \frac{54607676}{32805} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 27\) , \( -8\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+27{x}-8$ |
| 720.1-b3 |
720.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{4} \cdot 3^{8} \cdot 5^{4} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1.146228852$ |
$3.063150040$ |
4.441192498 |
\( \frac{3631696}{2025} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 2\) , \( 7\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+2{x}+7$ |
| 720.1-b4 |
720.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{8} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$2.292457704$ |
$1.531575020$ |
4.441192498 |
\( \frac{868327204}{5625} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -43\) , \( -92\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-43{x}-92$ |
| 720.1-b5 |
720.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{14} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$0.573114426$ |
$3.063150040$ |
4.441192498 |
\( \frac{24918016}{45} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -383\) , \( -3012\bigr] \) |
${y}^2={x}^3+{x}^2-383{x}-3012$ |
| 720.1-b6 |
720.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{10} \cdot 3^{2} \cdot 5^{4} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$4.584915408$ |
$0.765787510$ |
4.441192498 |
\( \frac{1770025017602}{75} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -793\) , \( -8042\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-793{x}-8042$ |
| 720.1-c1 |
720.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{12} \cdot 3^{32} \cdot 5^{2} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1$ |
$0.279462714$ |
2.827963832 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -436\) , \( -6160\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2-436{x}-6160$ |
| 720.1-c2 |
720.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{12} \cdot 3^{2} \cdot 5^{2} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.471403425$ |
2.827963832 |
\( -\frac{1}{15} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 4\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2+4{x}$ |
| 720.1-c3 |
720.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{16} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.558925428$ |
2.827963832 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 144\) , \( -504\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2+144{x}-504$ |
| 720.1-c4 |
720.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{12} \cdot 3^{8} \cdot 5^{8} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$1$ |
$1.117850856$ |
2.827963832 |
\( \frac{111284641}{50625} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -36\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2-36{x}$ |
| 720.1-c5 |
720.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{4} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$2.235701712$ |
2.827963832 |
\( \frac{13997521}{225} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -16\) , \( 56\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2-16{x}+56$ |
| 720.1-c6 |
720.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{12} \cdot 3^{16} \cdot 5^{4} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{6} \) |
$1$ |
$0.558925428$ |
2.827963832 |
\( \frac{272223782641}{164025} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -536\) , \( -4200\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2-536{x}-4200$ |
| 720.1-c7 |
720.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{12} \cdot 3^{2} \cdot 5^{2} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$1.117850856$ |
2.827963832 |
\( \frac{56667352321}{15} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -316\) , \( 2576\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2-316{x}+2576$ |
| 720.1-c8 |
720.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{12} \cdot 3^{8} \cdot 5^{2} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$16$ |
\( 2^{5} \) |
$1$ |
$0.279462714$ |
2.827963832 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -8636\) , \( -299040\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2-8636{x}-299040$ |
| 720.1-d1 |
720.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{48} \cdot 3^{2} \cdot 5^{6} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{3} \) |
$1$ |
$0.647145070$ |
3.683614316 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -216\) , \( 4080\bigr] \) |
${y}^2={x}^3-{x}^2-216{x}+4080$ |
| 720.1-d2 |
720.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{32} \cdot 3^{6} \cdot 5^{2} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1.941435210$ |
3.683614316 |
\( \frac{357911}{2160} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 24\) , \( -144\bigr] \) |
${y}^2={x}^3-{x}^2+24{x}-144$ |
| 720.1-d3 |
720.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{30} \cdot 3^{2} \cdot 5^{24} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$36$ |
\( 2^{3} \) |
$1$ |
$0.161786267$ |
3.683614316 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -7256\) , \( 34800\bigr] \) |
${y}^2={x}^3-{x}^2-7256{x}+34800$ |
| 720.1-d4 |
720.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{26} \cdot 3^{24} \cdot 5^{2} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$0.485358802$ |
3.683614316 |
\( \frac{35578826569}{5314410} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -1096\) , \( 12400\bigr] \) |
${y}^2={x}^3-{x}^2-1096{x}+12400$ |
| 720.1-d5 |
720.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{28} \cdot 3^{12} \cdot 5^{4} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.970717605$ |
3.683614316 |
\( \frac{702595369}{72900} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -296\) , \( -1680\bigr] \) |
${y}^2={x}^3-{x}^2-296{x}-1680$ |
| 720.1-d6 |
720.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{36} \cdot 3^{4} \cdot 5^{12} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$36$ |
\( 2^{4} \) |
$1$ |
$0.323572535$ |
3.683614316 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -5336\) , \( 151536\bigr] \) |
${y}^2={x}^3-{x}^2-5336{x}+151536$ |
| 720.1-d7 |
720.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{26} \cdot 3^{6} \cdot 5^{8} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.485358802$ |
3.683614316 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -4616\) , \( -119184\bigr] \) |
${y}^2={x}^3-{x}^2-4616{x}-119184$ |
| 720.1-d8 |
720.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{30} \cdot 3^{8} \cdot 5^{6} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{5} \) |
$1$ |
$0.161786267$ |
3.683614316 |
\( \frac{16778985534208729}{81000} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -85336\) , \( 9623536\bigr] \) |
${y}^2={x}^3-{x}^2-85336{x}+9623536$ |
| 720.1-e1 |
720.1-e |
$8$ |
$12$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{36} \cdot 3^{2} \cdot 5^{6} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1.344353050$ |
$0.647145070$ |
3.301385430 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -47\) , \( -454\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-47{x}-454$ |
| 720.1-e2 |
720.1-e |
$8$ |
$12$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{20} \cdot 3^{6} \cdot 5^{2} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.448117683$ |
$1.941435210$ |
3.301385430 |
\( \frac{357911}{2160} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 13\) , \( 14\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+13{x}+14$ |
| 720.1-e3 |
720.1-e |
$8$ |
$12$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{18} \cdot 3^{2} \cdot 5^{24} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \cdot 3 \) |
$5.377412203$ |
$0.161786267$ |
3.301385430 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -1807\) , \( -2534\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-1807{x}-2534$ |
| 720.1-e4 |
720.1-e |
$8$ |
$12$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{14} \cdot 3^{24} \cdot 5^{2} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{5} \cdot 3 \) |
$0.448117683$ |
$0.485358802$ |
3.301385430 |
\( \frac{35578826569}{5314410} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -267\) , \( -1274\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-267{x}-1274$ |
| 720.1-e5 |
720.1-e |
$8$ |
$12$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{16} \cdot 3^{12} \cdot 5^{4} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \cdot 3 \) |
$0.896235367$ |
$0.970717605$ |
3.301385430 |
\( \frac{702595369}{72900} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -67\) , \( 286\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-67{x}+286$ |
| 720.1-e6 |
720.1-e |
$8$ |
$12$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{24} \cdot 3^{4} \cdot 5^{12} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \cdot 3 \) |
$2.688706101$ |
$0.323572535$ |
3.301385430 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -1327\) , \( -17606\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-1327{x}-17606$ |
| 720.1-e7 |
720.1-e |
$8$ |
$12$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{14} \cdot 3^{6} \cdot 5^{8} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \cdot 3 \) |
$1.792470734$ |
$0.485358802$ |
3.301385430 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -1147\) , \( 16054\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-1147{x}+16054$ |
| 720.1-e8 |
720.1-e |
$8$ |
$12$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{18} \cdot 3^{8} \cdot 5^{6} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{5} \cdot 3 \) |
$1.344353050$ |
$0.161786267$ |
3.301385430 |
\( \frac{16778985534208729}{81000} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -21327\) , \( -1181606\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-21327{x}-1181606$ |
| 720.1-f1 |
720.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{24} \cdot 3^{32} \cdot 5^{2} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$3.714905803$ |
$0.279462714$ |
5.252809626 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1760\) , \( 52788\bigr] \) |
${y}^2={x}^3+{x}^2-1760{x}+52788$ |
| 720.1-f2 |
720.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{24} \cdot 3^{2} \cdot 5^{2} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.928726450$ |
$4.471403425$ |
5.252809626 |
\( -\frac{1}{15} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 0\) , \( -12\bigr] \) |
${y}^2={x}^3+{x}^2-12$ |
| 720.1-f3 |
720.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{24} \cdot 3^{4} \cdot 5^{16} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1.857452901$ |
$0.558925428$ |
5.252809626 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 560\) , \( 2900\bigr] \) |
${y}^2={x}^3+{x}^2+560{x}+2900$ |
| 720.1-f4 |
720.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{24} \cdot 3^{8} \cdot 5^{8} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$3.714905803$ |
$1.117850856$ |
5.252809626 |
\( \frac{111284641}{50625} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -160\) , \( 308\bigr] \) |
${y}^2={x}^3+{x}^2-160{x}+308$ |
| 720.1-f5 |
720.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{24} \cdot 3^{4} \cdot 5^{4} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1.857452901$ |
$2.235701712$ |
5.252809626 |
\( \frac{13997521}{225} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -80\) , \( -300\bigr] \) |
${y}^2={x}^3+{x}^2-80{x}-300$ |
| 720.1-f6 |
720.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{24} \cdot 3^{16} \cdot 5^{4} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{7} \) |
$1.857452901$ |
$0.558925428$ |
5.252809626 |
\( \frac{272223782641}{164025} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -2160\) , \( 37908\bigr] \) |
${y}^2={x}^3+{x}^2-2160{x}+37908$ |
| 720.1-f7 |
720.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{24} \cdot 3^{2} \cdot 5^{2} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$0.928726450$ |
$1.117850856$ |
5.252809626 |
\( \frac{56667352321}{15} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1280\) , \( -18060\bigr] \) |
${y}^2={x}^3+{x}^2-1280{x}-18060$ |
| 720.1-f8 |
720.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{24} \cdot 3^{8} \cdot 5^{2} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$3.714905803$ |
$0.279462714$ |
5.252809626 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -34560\) , \( 2461428\bigr] \) |
${y}^2={x}^3+{x}^2-34560{x}+2461428$ |
| 720.1-g1 |
720.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{22} \cdot 3^{2} \cdot 5^{16} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{6} \) |
$1$ |
$0.765787510$ |
3.874612377 |
\( -\frac{27995042}{1171875} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -80\) , \( 2400\bigr] \) |
${y}^2={x}^3-{x}^2-80{x}+2400$ |
| 720.1-g2 |
720.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{20} \cdot 3^{16} \cdot 5^{2} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.531575020$ |
3.874612377 |
\( \frac{54607676}{32805} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 80\) , \( -80\bigr] \) |
${y}^2={x}^3-{x}^2+80{x}-80$ |
| 720.1-g3 |
720.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{16} \cdot 3^{8} \cdot 5^{4} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$3.063150040$ |
3.874612377 |
\( \frac{3631696}{2025} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -20\) , \( 0\bigr] \) |
${y}^2={x}^3-{x}^2-20{x}$ |
| 720.1-g4 |
720.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{20} \cdot 3^{4} \cdot 5^{8} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$16$ |
\( 2^{5} \) |
$1$ |
$1.531575020$ |
3.874612377 |
\( \frac{868327204}{5625} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -200\) , \( 1152\bigr] \) |
${y}^2={x}^3-{x}^2-200{x}+1152$ |
| 720.1-g5 |
720.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{2} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$3.063150040$ |
3.874612377 |
\( \frac{24918016}{45} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -15\) , \( -18\bigr] \) |
${y}^2={x}^3-{x}^2-15{x}-18$ |
| 720.1-g6 |
720.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{22} \cdot 3^{2} \cdot 5^{4} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$16$ |
\( 2^{4} \) |
$1$ |
$0.765787510$ |
3.874612377 |
\( \frac{1770025017602}{75} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -3200\) , \( 70752\bigr] \) |
${y}^2={x}^3-{x}^2-3200{x}+70752$ |
| 720.1-h1 |
720.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$6.963173771$ |
4.403897772 |
\( \frac{21296}{15} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 8\) , \( 1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+8{x}+1$ |
| 720.1-h2 |
720.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{4} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$3.481586885$ |
4.403897772 |
\( \frac{470596}{225} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 3\) , \( 4\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+3{x}+4$ |
*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.
