| 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 |
| 72.1-a1 |
72.1-a |
$10$ |
$32$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$7.32059$ |
$(a^3-4a+1), (a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$4.037783633$ |
1.345927877 |
\( \frac{79558124472974}{3} a^{2} - \frac{21317535211108}{3} \) |
\( \bigl[a^{2} + a - 2\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( a + 1\) , \( 50 a^{3} - 9 a^{2} - 275 a - 135\) , \( 444 a^{3} - 83 a^{2} - 2421 a - 1171\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-1\right){x}^{2}+\left(50a^{3}-9a^{2}-275a-135\right){x}+444a^{3}-83a^{2}-2421a-1171$ |
| 72.1-a2 |
72.1-a |
$10$ |
$32$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{32} \) |
$7.32059$ |
$(a^3-4a+1), (a^2-2)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$64.60453813$ |
1.345927877 |
\( \frac{207646}{6561} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a^{3} - a^{2} - 3 a + 3\) , \( a^{2} + a - 2\) , \( 4 a^{3} + 8 a^{2} + 3 a + 6\) , \( 119 a^{3} + 247 a^{2} + 10 a - 43\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+3\right){x}^{2}+\left(4a^{3}+8a^{2}+3a+6\right){x}+119a^{3}+247a^{2}+10a-43$ |
| 72.1-a3 |
72.1-a |
$10$ |
$32$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{4} \) |
$7.32059$ |
$(a^3-4a+1), (a^2-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$258.4181525$ |
1.345927877 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -a^{2} + a + 2\) , \( a^{3} - 4 a + 1\) , \( 2 a^{2} + 2 a + 1\) , \( -2 a^{3} - 3 a^{2} + 3 a\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(2a^{2}+2a+1\right){x}-2a^{3}-3a^{2}+3a$ |
| 72.1-a4 |
72.1-a |
$10$ |
$32$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \) |
$7.32059$ |
$(a^3-4a+1), (a^2-2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$516.8363050$ |
1.345927877 |
\( \frac{35152}{9} \) |
\( \bigl[a^{3} - 3 a\) , \( 0\) , \( a^{3} - 3 a\) , \( -2\) , \( -1\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}-2{x}-1$ |
| 72.1-a5 |
72.1-a |
$10$ |
$32$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{16} \) |
$7.32059$ |
$(a^3-4a+1), (a^2-2)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1033.672610$ |
1.345927877 |
\( \frac{1556068}{81} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a^{3} - a^{2} - 3 a + 3\) , \( a^{2} + a - 2\) , \( -6 a^{3} - 17 a^{2} - 7 a + 6\) , \( 30 a^{3} + 57 a^{2} - 10 a - 15\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+3\right){x}^{2}+\left(-6a^{3}-17a^{2}-7a+6\right){x}+30a^{3}+57a^{2}-10a-15$ |
| 72.1-a6 |
72.1-a |
$10$ |
$32$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{4} \) |
$7.32059$ |
$(a^3-4a+1), (a^2-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$64.60453813$ |
1.345927877 |
\( \frac{28756228}{3} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a^{3} - a^{2} - 4 a + 3\) , \( a^{3} - 4 a + 1\) , \( 17 a^{3} - 42 a^{2} + 13 a + 6\) , \( 135 a^{3} - 290 a^{2} + 33 a + 44\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+3\right){x}^{2}+\left(17a^{3}-42a^{2}+13a+6\right){x}+135a^{3}-290a^{2}+33a+44$ |
| 72.1-a7 |
72.1-a |
$10$ |
$32$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \) |
$7.32059$ |
$(a^3-4a+1), (a^2-2)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1033.672610$ |
1.345927877 |
\( \frac{3065617154}{9} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a^{3} - a^{2} - 3 a + 3\) , \( a^{2} + a - 2\) , \( -96 a^{3} - 242 a^{2} - 97 a + 6\) , \( 2001 a^{3} + 4017 a^{2} - 190 a - 897\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+3\right){x}^{2}+\left(-96a^{3}-242a^{2}-97a+6\right){x}+2001a^{3}+4017a^{2}-190a-897$ |
| 72.1-a8 |
72.1-a |
$10$ |
$32$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$7.32059$ |
$(a^3-4a+1), (a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$4.037783633$ |
1.345927877 |
\( -\frac{79558124472974}{3} a^{2} + \frac{296914962680788}{3} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a^{3} - a^{2} - 3 a + 3\) , \( a^{3} - 4 a + 1\) , \( 74 a^{3} + 8 a^{2} - 346 a - 169\) , \( 644 a^{3} + 83 a^{2} - 3020 a - 1503\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+3\right){x}^{2}+\left(74a^{3}+8a^{2}-346a-169\right){x}+644a^{3}+83a^{2}-3020a-1503$ |
| 72.1-a9 |
72.1-a |
$10$ |
$32$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{4} \) |
$7.32059$ |
$(a^3-4a+1), (a^2-2)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$258.4181525$ |
1.345927877 |
\( \frac{123062343233293457}{3} a^{3} - 123062343233293457 a + 58012144939294440 \) |
\( \bigl[a^{2} + a - 2\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( a^{3} + a^{2} - 4 a - 2\) , \( 256 a^{3} + 2 a^{2} - 1483 a - 1022\) , \( -5108 a^{3} + 192 a^{2} + 27413 a + 15414\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-1\right){x}^{2}+\left(256a^{3}+2a^{2}-1483a-1022\right){x}-5108a^{3}+192a^{2}+27413a+15414$ |
| 72.1-a10 |
72.1-a |
$10$ |
$32$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{4} \) |
$7.32059$ |
$(a^3-4a+1), (a^2-2)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$258.4181525$ |
1.345927877 |
\( -\frac{123062343233293457}{3} a^{3} + 123062343233293457 a + 58012144939294440 \) |
\( \bigl[a^{2} + a - 2\) , \( a^{2} - a - 1\) , \( a^{3} + a^{2} - 4 a - 2\) , \( -255 a^{3} + 2 a^{2} + 1478 a - 1022\) , \( 5110 a^{3} + 192 a^{2} - 27420 a + 15414\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(-255a^{3}+2a^{2}+1478a-1022\right){x}+5110a^{3}+192a^{2}-27420a+15414$ |
| 72.1-b1 |
72.1-b |
$10$ |
$32$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$7.32059$ |
$(a^3-4a+1), (a^2-2)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.079273864$ |
$692.0865880$ |
1.945184808 |
\( \frac{79558124472974}{3} a^{2} - \frac{21317535211108}{3} \) |
\( \bigl[a^{3} - 4 a + 1\) , \( -a^{2} + 2\) , \( a^{2} - 1\) , \( 52 a^{3} - 11 a^{2} - 281 a - 132\) , \( -393 a^{3} + 73 a^{2} + 2143 a + 1036\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(52a^{3}-11a^{2}-281a-132\right){x}-393a^{3}+73a^{2}+2143a+1036$ |
| 72.1-b2 |
72.1-b |
$10$ |
$32$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{32} \) |
$7.32059$ |
$(a^3-4a+1), (a^2-2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1.079273864$ |
$10.81385293$ |
1.945184808 |
\( \frac{207646}{6561} \) |
\( \bigl[a + 1\) , \( a^{2} - a - 2\) , \( a^{3} - 3 a\) , \( 3 a^{3} + 10 a^{2} + 6 a + 1\) , \( -116 a^{3} - 238 a^{2} - 4 a + 45\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(3a^{3}+10a^{2}+6a+1\right){x}-116a^{3}-238a^{2}-4a+45$ |
| 72.1-b3 |
72.1-b |
$10$ |
$32$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{4} \) |
$7.32059$ |
$(a^3-4a+1), (a^2-2)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.539636932$ |
$692.0865880$ |
1.945184808 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( a^{2} - a - 2\) , \( a^{2} + a - 2\) , \( 2 a^{2} + 2 a + 1\) , \( a^{3} + 3 a^{2} - 2\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(2a^{2}+2a+1\right){x}+a^{3}+3a^{2}-2$ |
| 72.1-b4 |
72.1-b |
$10$ |
$32$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \) |
$7.32059$ |
$(a^3-4a+1), (a^2-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.269818466$ |
$1384.173176$ |
1.945184808 |
\( \frac{35152}{9} \) |
\( \bigl[a^{3} - 3 a\) , \( -1\) , \( a^{3} - 3 a\) , \( -2\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}-{x}^{2}-2{x}$ |
| 72.1-b5 |
72.1-b |
$10$ |
$32$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{16} \) |
$7.32059$ |
$(a^3-4a+1), (a^2-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.539636932$ |
$173.0216470$ |
1.945184808 |
\( \frac{1556068}{81} \) |
\( \bigl[a + 1\) , \( a^{2} - a - 2\) , \( a^{3} - 3 a\) , \( -7 a^{3} - 15 a^{2} - 4 a + 1\) , \( -37 a^{3} - 73 a^{2} + 6 a + 17\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-7a^{3}-15a^{2}-4a+1\right){x}-37a^{3}-73a^{2}+6a+17$ |
| 72.1-b6 |
72.1-b |
$10$ |
$32$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{4} \) |
$7.32059$ |
$(a^3-4a+1), (a^2-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.539636932$ |
$2768.346352$ |
1.945184808 |
\( \frac{28756228}{3} \) |
\( \bigl[a + 1\) , \( a^{2} - 2\) , \( a^{2} - 1\) , \( 16 a^{3} - 40 a^{2} + 16 a + 1\) , \( -119 a^{3} + 249 a^{2} - 16 a - 42\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(16a^{3}-40a^{2}+16a+1\right){x}-119a^{3}+249a^{2}-16a-42$ |
| 72.1-b7 |
72.1-b |
$10$ |
$32$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \) |
$7.32059$ |
$(a^3-4a+1), (a^2-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1.079273864$ |
$10.81385293$ |
1.945184808 |
\( \frac{3065617154}{9} \) |
\( \bigl[a + 1\) , \( a^{2} - a - 2\) , \( a^{3} - 3 a\) , \( -97 a^{3} - 240 a^{2} - 94 a + 1\) , \( -2098 a^{3} - 4258 a^{2} + 96 a + 899\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-97a^{3}-240a^{2}-94a+1\right){x}-2098a^{3}-4258a^{2}+96a+899$ |
| 72.1-b8 |
72.1-b |
$10$ |
$32$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$7.32059$ |
$(a^3-4a+1), (a^2-2)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.079273864$ |
$692.0865880$ |
1.945184808 |
\( -\frac{79558124472974}{3} a^{2} + \frac{296914962680788}{3} \) |
\( \bigl[a + 1\) , \( a^{2} - a - 2\) , \( a^{2} - 1\) , \( 73 a^{3} + 10 a^{2} - 345 a - 174\) , \( -571 a^{3} - 74 a^{2} + 2677 a + 1330\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(73a^{3}+10a^{2}-345a-174\right){x}-571a^{3}-74a^{2}+2677a+1330$ |
| 72.1-b9 |
72.1-b |
$10$ |
$32$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{4} \) |
$7.32059$ |
$(a^3-4a+1), (a^2-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$2.158547729$ |
$0.675865808$ |
1.945184808 |
\( \frac{123062343233293457}{3} a^{3} - 123062343233293457 a + 58012144939294440 \) |
\( \bigl[a^{3} - 4 a + 1\) , \( -a^{2} + 2\) , \( a^{3} - 3 a\) , \( 256 a^{3} - 1483 a - 1019\) , \( 5365 a^{3} - 191 a^{2} - 28899 a - 16436\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(256a^{3}-1483a-1019\right){x}+5365a^{3}-191a^{2}-28899a-16436$ |
| 72.1-b10 |
72.1-b |
$10$ |
$32$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{4} \) |
$7.32059$ |
$(a^3-4a+1), (a^2-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$2.158547729$ |
$0.675865808$ |
1.945184808 |
\( -\frac{123062343233293457}{3} a^{3} + 123062343233293457 a + 58012144939294440 \) |
\( \bigl[a^{3} - 4 a + 1\) , \( -a^{3} - a^{2} + 4 a + 2\) , \( a^{3} - 3 a\) , \( -257 a^{3} + 1486 a - 1019\) , \( -5365 a^{3} - 191 a^{2} + 28899 a - 16436\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+2\right){x}^{2}+\left(-257a^{3}+1486a-1019\right){x}-5365a^{3}-191a^{2}+28899a-16436$ |
*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.
