| 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 |
| 1458.1-a1 |
1458.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{6} \cdot 3^{18} \) |
$1.56179$ |
$(a), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$0.142994828$ |
$2.712811098$ |
1.645796510 |
\( \frac{23031}{8} a - \frac{2997}{8} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 27 a - 42\) , \( 108 a - 154\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(27a-42\right){x}+108a-154$ |
| 1458.1-a2 |
1458.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{2} \cdot 3^{6} \) |
$1.56179$ |
$(a), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$0.428984485$ |
$24.41529989$ |
1.645796510 |
\( \frac{2023731}{2} a + \frac{2864997}{2} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -3 a + 3\) , \( 1\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-3a+3\right){x}+1$ |
| 1458.1-b1 |
1458.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{3} \cdot 3^{6} \) |
$1.56179$ |
$(a), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$34.46743844$ |
1.354008858 |
\( \frac{7196661}{4} a - \frac{5095683}{2} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -3 a - 6\) , \( 6 a + 10\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-3a-6\right){x}+6a+10$ |
| 1458.1-b2 |
1458.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{9} \cdot 3^{18} \) |
$1.56179$ |
$(a), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$3.829715382$ |
1.354008858 |
\( \frac{15579}{32} a + \frac{11097}{16} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 27 a + 39\) , \( -54 a - 73\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(27a+39\right){x}-54a-73$ |
| 1458.1-c1 |
1458.1-c |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{6} \cdot 3^{6} \) |
$1.56179$ |
$(a), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.238612220$ |
$28.07285199$ |
3.157715233 |
\( \frac{23031}{8} a - \frac{2997}{8} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 3 a - 5\) , \( -5 a + 7\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(3a-5\right){x}-5a+7$ |
| 1458.1-c2 |
1458.1-c |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{2} \cdot 3^{18} \) |
$1.56179$ |
$(a), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$0.715836662$ |
$3.119205777$ |
3.157715233 |
\( \frac{2023731}{2} a + \frac{2864997}{2} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -27 a + 25\) , \( 27 a - 53\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-27a+25\right){x}+27a-53$ |
| 1458.1-d1 |
1458.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{3} \cdot 3^{18} \) |
$1.56179$ |
$(a), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3^{2} \) |
$1$ |
$0.881741077$ |
2.805682928 |
\( \frac{7196661}{4} a - \frac{5095683}{2} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -27 a - 56\) , \( -135 a - 215\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-27a-56\right){x}-135a-215$ |
| 1458.1-d2 |
1458.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{9} \cdot 3^{6} \) |
$1.56179$ |
$(a), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$7.935669699$ |
2.805682928 |
\( \frac{15579}{32} a + \frac{11097}{16} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 3 a + 4\) , \( a + 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(3a+4\right){x}+a+1$ |
| 1458.1-e1 |
1458.1-e |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2 \cdot 3^{6} \) |
$1.56179$ |
$(a), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$23.90269615$ |
0.938986585 |
\( -\frac{355725}{2} a - 250047 \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -2 a\) , \( a\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}-2a{x}+a$ |
| 1458.1-e2 |
1458.1-e |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{3} \cdot 3^{18} \) |
$1.56179$ |
$(a), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$2.655855128$ |
0.938986585 |
\( \frac{47277}{4} a - \frac{32859}{2} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 13 a - 15\) , \( 27 a - 33\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(13a-15\right){x}+27a-33$ |
| 1458.1-f1 |
1458.1-f |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2 \cdot 3^{18} \) |
$1.56179$ |
$(a), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$2.453082648$ |
2.601887063 |
\( -\frac{93339}{2} a + 53244 \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -14 a - 29\) , \( -41 a - 67\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-14a-29\right){x}-41a-67$ |
| 1458.1-f2 |
1458.1-f |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{3} \cdot 3^{6} \) |
$1.56179$ |
$(a), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$22.07774383$ |
2.601887063 |
\( -\frac{34371}{4} a + 13878 \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( a + 1\) , \( -a - 1\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(a+1\right){x}-a-1$ |
| 1458.1-g1 |
1458.1-g |
$3$ |
$9$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{2} \cdot 3^{18} \) |
$1.56179$ |
$(a), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$1.061975282$ |
2.252789771 |
\( -\frac{132651}{2} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -29\) , \( -53\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-29{x}-53$ |
| 1458.1-g2 |
1458.1-g |
$3$ |
$9$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{18} \cdot 3^{10} \) |
$1.56179$ |
$(a), (3)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{3} \) |
$1$ |
$9.557777544$ |
2.252789771 |
\( -\frac{1167051}{512} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -14\) , \( 29\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-14{x}+29$ |
| 1458.1-g3 |
1458.1-g |
$3$ |
$9$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{6} \cdot 3^{6} \) |
$1.56179$ |
$(a), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$9.557777544$ |
2.252789771 |
\( \frac{9261}{8} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 1\) , \( -1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+{x}-1$ |
| 1458.1-h1 |
1458.1-h |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{3} \cdot 3^{6} \) |
$1.56179$ |
$(a), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$18.99297365$ |
2.238343411 |
\( -\frac{47277}{4} a - \frac{32859}{2} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -2 a - 2\) , \( a + 1\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-2a-2\right){x}+a+1$ |
| 1458.1-h2 |
1458.1-h |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2 \cdot 3^{18} \) |
$1.56179$ |
$(a), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$2.110330406$ |
2.238343411 |
\( \frac{355725}{2} a - 250047 \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 13 a - 2\) , \( 13 a - 13\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(13a-2\right){x}+13a-13$ |
| 1458.1-i1 |
1458.1-i |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2 \cdot 3^{18} \) |
$1.56179$ |
$(a), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$2.110330406$ |
2.238343411 |
\( -\frac{355725}{2} a - 250047 \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -14 a - 2\) , \( -14 a - 13\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-14a-2\right){x}-14a-13$ |
| 1458.1-i2 |
1458.1-i |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{3} \cdot 3^{6} \) |
$1.56179$ |
$(a), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$18.99297365$ |
2.238343411 |
\( \frac{47277}{4} a - \frac{32859}{2} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( a - 2\) , \( -2 a + 1\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(a-2\right){x}-2a+1$ |
| 1458.1-j1 |
1458.1-j |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{15} \cdot 3^{18} \) |
$1.56179$ |
$(a), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$2.202485858$ |
0.778696342 |
\( \frac{211977}{256} a + \frac{46143}{64} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -20 a - 41\) , \( 13 a - 18\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-20a-41\right){x}+13a-18$ |
| 1458.1-j2 |
1458.1-j |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{5} \cdot 3^{6} \) |
$1.56179$ |
$(a), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$19.82237272$ |
0.778696342 |
\( \frac{2076705297}{8} a + \frac{734226957}{2} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -20 a - 26\) , \( 38 a + 54\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-20a-26\right){x}+38a+54$ |
| 1458.1-k1 |
1458.1-k |
$3$ |
$9$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{2} \cdot 3^{6} \) |
$1.56179$ |
$(a), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$0.282606480$ |
$39.86878607$ |
1.770466107 |
\( -\frac{132651}{2} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-3{x}+3$ |
| 1458.1-k2 |
1458.1-k |
$3$ |
$9$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{18} \cdot 3^{22} \) |
$1.56179$ |
$(a), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$2.543458324$ |
$0.492207235$ |
1.770466107 |
\( -\frac{1167051}{512} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -123\) , \( -667\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-123{x}-667$ |
| 1458.1-k3 |
1458.1-k |
$3$ |
$9$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{6} \cdot 3^{18} \) |
$1.56179$ |
$(a), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.847819441$ |
$4.429865119$ |
1.770466107 |
\( \frac{9261}{8} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 12\) , \( 8\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+12{x}+8$ |
| 1458.1-l1 |
1458.1-l |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2 \cdot 3^{6} \) |
$1.56179$ |
$(a), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$0.580581349$ |
$41.41898079$ |
1.889317647 |
\( -\frac{93339}{2} a + 53244 \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -2 a - 3\) , \( 2 a + 3\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-2a-3\right){x}+2a+3$ |
| 1458.1-l2 |
1458.1-l |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{3} \cdot 3^{18} \) |
$1.56179$ |
$(a), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$0.193527116$ |
$4.602108976$ |
1.889317647 |
\( -\frac{34371}{4} a + 13878 \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 13 a + 12\) , \( -6\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(13a+12\right){x}-6$ |
| 1458.1-m1 |
1458.1-m |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{3} \cdot 3^{18} \) |
$1.56179$ |
$(a), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$2.655855128$ |
0.938986585 |
\( -\frac{47277}{4} a - \frac{32859}{2} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -14 a - 15\) , \( -27 a - 33\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-14a-15\right){x}-27a-33$ |
| 1458.1-m2 |
1458.1-m |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2 \cdot 3^{6} \) |
$1.56179$ |
$(a), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$23.90269615$ |
0.938986585 |
\( \frac{355725}{2} a - 250047 \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( a\) , \( -a\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+a{x}-a$ |
| 1458.1-n1 |
1458.1-n |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{15} \cdot 3^{6} \) |
$1.56179$ |
$(a), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \cdot 5 \) |
$0.198393287$ |
$13.45531707$ |
3.145970620 |
\( \frac{211977}{256} a + \frac{46143}{64} \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( -2 a - 4\) , \( -4 a - 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-2a-4\right){x}-4a-4$ |
| 1458.1-n2 |
1458.1-n |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{5} \cdot 3^{18} \) |
$1.56179$ |
$(a), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 5 \) |
$0.595179863$ |
$1.495035230$ |
3.145970620 |
\( \frac{2076705297}{8} a + \frac{734226957}{2} \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( -182 a - 244\) , \( -1688 a - 2428\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-182a-244\right){x}-1688a-2428$ |
| 1458.1-o1 |
1458.1-o |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{4} \cdot 3^{6} \) |
$1.56179$ |
$(a), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$19.02486084$ |
1.494734235 |
\( -\frac{978710587695}{4} a - \frac{1384105779837}{4} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( 31 a - 53\) , \( -10 a + 18\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(31a-53\right){x}-10a+18$ |
| 1458.1-o2 |
1458.1-o |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{12} \cdot 3^{18} \) |
$1.56179$ |
$(a), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$2.113873427$ |
1.494734235 |
\( -\frac{4091893011}{64} a + \frac{5786290701}{64} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -68 a - 258\) , \( 1296 a + 1074\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-68a-258\right){x}+1296a+1074$ |
| 1458.1-p1 |
1458.1-p |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{4} \cdot 3^{18} \) |
$1.56179$ |
$(a), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.737103634$ |
3.127265868 |
\( \frac{978710587695}{4} a - \frac{1384105779837}{4} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -276 a - 486\) , \( -68 a - 416\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-276a-486\right){x}-68a-416$ |
| 1458.1-p2 |
1458.1-p |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{12} \cdot 3^{6} \) |
$1.56179$ |
$(a), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$6.633932707$ |
3.127265868 |
\( \frac{4091893011}{64} a + \frac{5786290701}{64} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 7 a - 29\) , \( 45 a - 31\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(7a-29\right){x}+45a-31$ |
| 1458.1-q1 |
1458.1-q |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{3} \cdot 3^{6} \) |
$1.56179$ |
$(a), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$34.46743844$ |
1.354008858 |
\( -\frac{7196661}{4} a - \frac{5095683}{2} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 3 a - 6\) , \( -6 a + 10\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(3a-6\right){x}-6a+10$ |
| 1458.1-q2 |
1458.1-q |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{9} \cdot 3^{18} \) |
$1.56179$ |
$(a), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$3.829715382$ |
1.354008858 |
\( -\frac{15579}{32} a + \frac{11097}{16} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -27 a + 39\) , \( 54 a - 73\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-27a+39\right){x}+54a-73$ |
| 1458.1-r1 |
1458.1-r |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{3} \cdot 3^{18} \) |
$1.56179$ |
$(a), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3^{2} \) |
$1$ |
$0.881741077$ |
2.805682928 |
\( -\frac{7196661}{4} a - \frac{5095683}{2} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 27 a - 56\) , \( 135 a - 215\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(27a-56\right){x}+135a-215$ |
| 1458.1-r2 |
1458.1-r |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{9} \cdot 3^{6} \) |
$1.56179$ |
$(a), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$7.935669699$ |
2.805682928 |
\( -\frac{15579}{32} a + \frac{11097}{16} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3 a + 4\) , \( -a + 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-3a+4\right){x}-a+1$ |
| 1458.1-s1 |
1458.1-s |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{4} \cdot 3^{18} \) |
$1.56179$ |
$(a), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.737103634$ |
3.127265868 |
\( -\frac{978710587695}{4} a - \frac{1384105779837}{4} \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( 277 a - 487\) , \( -419 a + 137\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(277a-487\right){x}-419a+137$ |
| 1458.1-s2 |
1458.1-s |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{12} \cdot 3^{6} \) |
$1.56179$ |
$(a), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$6.633932707$ |
3.127265868 |
\( -\frac{4091893011}{64} a + \frac{5786290701}{64} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -8 a - 29\) , \( -46 a - 31\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-8a-29\right){x}-46a-31$ |
| 1458.1-t1 |
1458.1-t |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{4} \cdot 3^{6} \) |
$1.56179$ |
$(a), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$19.02486084$ |
1.494734235 |
\( \frac{978710587695}{4} a - \frac{1384105779837}{4} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -31 a - 54\) , \( -44 a - 44\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-31a-54\right){x}-44a-44$ |
| 1458.1-t2 |
1458.1-t |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{12} \cdot 3^{18} \) |
$1.56179$ |
$(a), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$2.113873427$ |
1.494734235 |
\( \frac{4091893011}{64} a + \frac{5786290701}{64} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 67 a - 258\) , \( -1296 a + 1074\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(67a-258\right){x}-1296a+1074$ |
| 1458.1-u1 |
1458.1-u |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{3} \cdot 3^{6} \) |
$1.56179$ |
$(a), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$22.07774383$ |
2.601887063 |
\( \frac{34371}{4} a + 13878 \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -2 a + 1\) , \( -1\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-2a+1\right){x}-1$ |
| 1458.1-u2 |
1458.1-u |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2 \cdot 3^{18} \) |
$1.56179$ |
$(a), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$2.453082648$ |
2.601887063 |
\( \frac{93339}{2} a + 53244 \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 13 a - 29\) , \( 40 a - 67\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(13a-29\right){x}+40a-67$ |
| 1458.1-v1 |
1458.1-v |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{3} \cdot 3^{18} \) |
$1.56179$ |
$(a), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$0.193527116$ |
$4.602108976$ |
1.889317647 |
\( \frac{34371}{4} a + 13878 \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -14 a + 12\) , \( -6\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-14a+12\right){x}-6$ |
| 1458.1-v2 |
1458.1-v |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2 \cdot 3^{6} \) |
$1.56179$ |
$(a), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$0.580581349$ |
$41.41898079$ |
1.889317647 |
\( \frac{93339}{2} a + 53244 \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( a - 3\) , \( -2 a + 3\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(a-3\right){x}-2a+3$ |
| 1458.1-w1 |
1458.1-w |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{6} \cdot 3^{18} \) |
$1.56179$ |
$(a), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$0.142994828$ |
$2.712811098$ |
1.645796510 |
\( -\frac{23031}{8} a - \frac{2997}{8} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -27 a - 42\) , \( -108 a - 154\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-27a-42\right){x}-108a-154$ |
| 1458.1-w2 |
1458.1-w |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{2} \cdot 3^{6} \) |
$1.56179$ |
$(a), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$0.428984485$ |
$24.41529989$ |
1.645796510 |
\( -\frac{2023731}{2} a + \frac{2864997}{2} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 3 a + 3\) , \( 1\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(3a+3\right){x}+1$ |
| 1458.1-x1 |
1458.1-x |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{15} \cdot 3^{6} \) |
$1.56179$ |
$(a), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \cdot 5 \) |
$0.198393287$ |
$13.45531707$ |
3.145970620 |
\( -\frac{211977}{256} a + \frac{46143}{64} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 3 a - 3\) , \( 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(3a-3\right){x}+1$ |
| 1458.1-x2 |
1458.1-x |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{5} \cdot 3^{18} \) |
$1.56179$ |
$(a), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 5 \) |
$0.595179863$ |
$1.495035230$ |
3.145970620 |
\( -\frac{2076705297}{8} a + \frac{734226957}{2} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 183 a - 243\) , \( 1444 a - 2063\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(183a-243\right){x}+1444a-2063$ |
*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.
