| 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 |
| 1024.1-a1 |
1024.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{14} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$17.06626753$ |
2.463303538 |
\( -512 a + 512 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+2{x}$ |
| 1024.1-a2 |
1024.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{22} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$17.06626753$ |
2.463303538 |
\( 249872 a + 434912 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -8\) , \( 8 a + 8\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-8{x}+8a+8$ |
| 1024.1-b1 |
1024.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{14} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.381218488$ |
$8.846686439$ |
3.527381188 |
\( -512 a + 512 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -2 a - 3\) , \( -4 a - 7\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-2a-3\right){x}-4a-7$ |
| 1024.1-b2 |
1024.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{22} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.690609244$ |
$8.846686439$ |
3.527381188 |
\( 249872 a + 434912 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -42 a - 73\) , \( -182 a - 315\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-42a-73\right){x}-182a-315$ |
| 1024.1-c1 |
1024.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( - 2^{23} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.276710919$ |
1.523255234 |
\( -2002968 a + 3470040 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 1642 a - 2843\) , \( 48607 a - 84190\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(1642a-2843\right){x}+48607a-84190$ |
| 1024.1-c2 |
1024.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{16} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$21.10684367$ |
1.523255234 |
\( 3456 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 112 a - 193\) , \( 665 a - 1152\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(112a-193\right){x}+665a-1152$ |
| 1024.1-c3 |
1024.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{14} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$21.10684367$ |
1.523255234 |
\( 23328 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 12 a - 20\) , \( -22 a + 38\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(12a-20\right){x}-22a+38$ |
| 1024.1-c4 |
1024.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( - 2^{23} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$10.55342183$ |
1.523255234 |
\( 2002968 a + 3470040 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -298 a + 517\) , \( 3807 a - 6594\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-298a+517\right){x}+3807a-6594$ |
| 1024.1-d1 |
1024.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( - 2^{23} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.741115149$ |
$10.55342183$ |
2.652162765 |
\( -2002968 a + 3470040 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 118 a - 203\) , \( -849 a + 1470\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(118a-203\right){x}-849a+1470$ |
| 1024.1-d2 |
1024.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{16} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.870557574$ |
$21.10684367$ |
2.652162765 |
\( 3456 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 8 a - 13\) , \( -7 a + 12\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(8a-13\right){x}-7a+12$ |
| 1024.1-d3 |
1024.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{14} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.435278787$ |
$21.10684367$ |
2.652162765 |
\( 23328 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -2\) , \( 2 a\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}-2{x}+2a$ |
| 1024.1-d4 |
1024.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( - 2^{23} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.741115149$ |
$5.276710919$ |
2.652162765 |
\( 2002968 a + 3470040 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -22 a + 37\) , \( -89 a + 154\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-22a+37\right){x}-89a+154$ |
| 1024.1-e1 |
1024.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{16} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$16.29302268$ |
2.351695258 |
\( 128 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -2 a + 6\) , \( -12 a + 20\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a+6\right){x}-12a+20$ |
| 1024.1-e2 |
1024.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{14} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$32.58604536$ |
2.351695258 |
\( 10976 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -2\) , \( 2\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-2{x}+2$ |
| 1024.1-f1 |
1024.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{16} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.632943382$ |
$7.547952572$ |
3.558030500 |
\( 128 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -38 a + 66\) , \( 612 a - 1060\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-38a+66\right){x}+612a-1060$ |
| 1024.1-f2 |
1024.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{14} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.816471691$ |
$15.09590514$ |
3.558030500 |
\( 10976 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 10 a - 15\) , \( 21 a - 37\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(10a-15\right){x}+21a-37$ |
| 1024.1-g1 |
1024.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{14} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$8.846686439$ |
1.276909199 |
\( 512 a + 512 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+2{x}$ |
| 1024.1-g2 |
1024.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{22} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$8.846686439$ |
1.276909199 |
\( -249872 a + 434912 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -8\) , \( 8 a - 8\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}-8{x}+8a-8$ |
| 1024.1-h1 |
1024.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$9.722981027$ |
1.403391428 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 a + 4\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-2a+4\right){x}$ |
| 1024.1-h2 |
1024.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$19.44596205$ |
1.403391428 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 30 a - 52\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(30a-52\right){x}$ |
| 1024.1-h3 |
1024.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{24} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$9.722981027$ |
1.403391428 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 330 a - 572\) , \( 4284 a - 7420\bigr] \) |
${y}^2={x}^{3}+\left(330a-572\right){x}+4284a-7420$ |
| 1024.1-h4 |
1024.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{24} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$9.722981027$ |
1.403391428 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 330 a - 572\) , \( -4284 a + 7420\bigr] \) |
${y}^2={x}^{3}+\left(330a-572\right){x}-4284a+7420$ |
| 1024.1-i1 |
1024.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{14} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.399627251$ |
$17.06626753$ |
1.968806443 |
\( 512 a + 512 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 2 a - 3\) , \( -4 a + 7\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(2a-3\right){x}-4a+7$ |
| 1024.1-i2 |
1024.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{22} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.199813625$ |
$17.06626753$ |
1.968806443 |
\( -249872 a + 434912 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 42 a - 73\) , \( -182 a + 315\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(42a-73\right){x}-182a+315$ |
| 1024.1-j1 |
1024.1-j |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{14} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.429957487$ |
$21.67189957$ |
2.689873605 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 1\) , \( a + 2\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+{x}+a+2$ |
| 1024.1-j2 |
1024.1-j |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{14} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.289872463$ |
$7.223966526$ |
2.689873605 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 1\) , \( -a - 2\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+{x}-a-2$ |
| 1024.1-j3 |
1024.1-j |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{26} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-48$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.429957487$ |
$10.83594978$ |
2.689873605 |
\( -818626500 a + 1417905000 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -10 a - 59\) , \( -49 a - 2\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-10a-59\right){x}-49a-2$ |
| 1024.1-j4 |
1024.1-j |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{26} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-48$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1.289872463$ |
$3.611983263$ |
2.689873605 |
\( -818626500 a + 1417905000 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -10 a - 59\) , \( 49 a + 2\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-10a-59\right){x}+49a+2$ |
| 1024.1-j5 |
1024.1-j |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{22} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.859914975$ |
$21.67189957$ |
2.689873605 |
\( 54000 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -10 a - 19\) , \( 31 a + 54\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-10a-19\right){x}+31a+54$ |
| 1024.1-j6 |
1024.1-j |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{22} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$2.579744927$ |
$7.223966526$ |
2.689873605 |
\( 54000 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -10 a - 19\) , \( -31 a - 54\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-10a-19\right){x}-31a-54$ |
| 1024.1-j7 |
1024.1-j |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{26} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-48$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.429957487$ |
$10.83594978$ |
2.689873605 |
\( 818626500 a + 1417905000 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -170 a - 299\) , \( 1711 a + 2958\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-170a-299\right){x}+1711a+2958$ |
| 1024.1-j8 |
1024.1-j |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{26} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-48$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1.289872463$ |
$3.611983263$ |
2.689873605 |
\( 818626500 a + 1417905000 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -170 a - 299\) , \( -1711 a - 2958\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-170a-299\right){x}-1711a-2958$ |
| 1024.1-k1 |
1024.1-k |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{14} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.289872463$ |
$7.223966526$ |
2.689873605 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 1\) , \( a - 2\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+{x}+a-2$ |
| 1024.1-k2 |
1024.1-k |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{14} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.429957487$ |
$21.67189957$ |
2.689873605 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 1\) , \( -a + 2\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+{x}-a+2$ |
| 1024.1-k3 |
1024.1-k |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{26} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-48$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1.289872463$ |
$3.611983263$ |
2.689873605 |
\( -818626500 a + 1417905000 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 170 a - 299\) , \( 1711 a - 2958\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(170a-299\right){x}+1711a-2958$ |
| 1024.1-k4 |
1024.1-k |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{26} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-48$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.429957487$ |
$10.83594978$ |
2.689873605 |
\( -818626500 a + 1417905000 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 170 a - 299\) , \( -1711 a + 2958\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(170a-299\right){x}-1711a+2958$ |
| 1024.1-k5 |
1024.1-k |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{22} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$2.579744927$ |
$7.223966526$ |
2.689873605 |
\( 54000 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 10 a - 19\) , \( 31 a - 54\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(10a-19\right){x}+31a-54$ |
| 1024.1-k6 |
1024.1-k |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{22} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.859914975$ |
$21.67189957$ |
2.689873605 |
\( 54000 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 10 a - 19\) , \( -31 a + 54\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(10a-19\right){x}-31a+54$ |
| 1024.1-k7 |
1024.1-k |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{26} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-48$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1.289872463$ |
$3.611983263$ |
2.689873605 |
\( 818626500 a + 1417905000 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 10 a - 59\) , \( -49 a + 2\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(10a-59\right){x}-49a+2$ |
| 1024.1-k8 |
1024.1-k |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{26} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-48$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.429957487$ |
$10.83594978$ |
2.689873605 |
\( 818626500 a + 1417905000 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 10 a - 59\) , \( 49 a - 2\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(10a-59\right){x}+49a-2$ |
| 1024.1-l1 |
1024.1-l |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{14} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$17.06626753$ |
2.463303538 |
\( 512 a + 512 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+2{x}$ |
| 1024.1-l2 |
1024.1-l |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{22} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$17.06626753$ |
2.463303538 |
\( -249872 a + 434912 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -8\) , \( -8 a + 8\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}-8{x}-8a+8$ |
| 1024.1-m1 |
1024.1-m |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$9.722981027$ |
1.403391428 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 a + 4\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(2a+4\right){x}$ |
| 1024.1-m2 |
1024.1-m |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$19.44596205$ |
1.403391428 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 a - 4\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(2a-4\right){x}$ |
| 1024.1-m3 |
1024.1-m |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{24} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$9.722981027$ |
1.403391428 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 22 a - 44\) , \( 84 a - 140\bigr] \) |
${y}^2={x}^{3}+\left(22a-44\right){x}+84a-140$ |
| 1024.1-m4 |
1024.1-m |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{24} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$9.722981027$ |
1.403391428 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 22 a - 44\) , \( -84 a + 140\bigr] \) |
${y}^2={x}^{3}+\left(22a-44\right){x}-84a+140$ |
| 1024.1-n1 |
1024.1-n |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{14} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.381218488$ |
$8.846686439$ |
3.527381188 |
\( 512 a + 512 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 2 a - 3\) , \( 4 a - 7\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(2a-3\right){x}+4a-7$ |
| 1024.1-n2 |
1024.1-n |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{22} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.690609244$ |
$8.846686439$ |
3.527381188 |
\( -249872 a + 434912 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 42 a - 73\) , \( 182 a - 315\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(42a-73\right){x}+182a-315$ |
| 1024.1-o1 |
1024.1-o |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{16} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$7.547952572$ |
1.089453112 |
\( 128 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2 a + 6\) , \( 12 a - 20\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a+6\right){x}+12a-20$ |
| 1024.1-o2 |
1024.1-o |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{14} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$15.09590514$ |
1.089453112 |
\( 10976 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -2\) , \( -2\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-2{x}-2$ |
*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.
