| 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 |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( - 2^{14} \) |
$1.42974$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$18.71292406$ |
1.654004437 |
\( -38944 a + 56032 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 2 a + 2\) , \( -2 a - 2\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(2a+2\right){x}-2a-2$ |
| 1024.1-a2 |
1024.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{16} \) |
$1.42974$ |
$(a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$18.71292406$ |
1.654004437 |
\( 384 a + 2432 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -2 a - 3\) , \( -2 a - 3\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-2a-3\right){x}-2a-3$ |
| 1024.1-a3 |
1024.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{23} \) |
$1.42974$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$9.356462031$ |
1.654004437 |
\( -274424 a + 418576 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -12 a - 23\) , \( 32 a + 37\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-12a-23\right){x}+32a+37$ |
| 1024.1-a4 |
1024.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( - 2^{23} \) |
$1.42974$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.678231015$ |
1.654004437 |
\( 1609752 a + 2278112 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -24 a + 32\) , \( 32 a - 48\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-24a+32\right){x}+32a-48$ |
| 1024.1-b1 |
1024.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( - 2^{23} \) |
$1.42974$ |
$(a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.031810300$ |
$11.41527282$ |
2.082145936 |
\( -1609752 a + 2278112 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 10 a - 1\) , \( -7 a + 15\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(10a-1\right){x}-7a+15$ |
| 1024.1-b2 |
1024.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{16} \) |
$1.42974$ |
$(a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.515905150$ |
$22.83054565$ |
2.082145936 |
\( -384 a + 2432 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -1\) , \( -a - 1\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-{x}-a-1$ |
| 1024.1-b3 |
1024.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( - 2^{14} \) |
$1.42974$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.257952575$ |
$22.83054565$ |
2.082145936 |
\( 38944 a + 56032 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -2 a - 2\) , \( 4 a + 6\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a-2\right){x}+4a+6$ |
| 1024.1-b4 |
1024.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{23} \) |
$1.42974$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.031810300$ |
$5.707636413$ |
2.082145936 |
\( 274424 a + 418576 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -10 a - 21\) , \( -39 a - 61\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-10a-21\right){x}-39a-61$ |
| 1024.1-c1 |
1024.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( - 2^{14} \) |
$1.42974$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.257952575$ |
$22.83054565$ |
2.082145936 |
\( -38944 a + 56032 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 2 a - 2\) , \( -4 a + 6\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(2a-2\right){x}-4a+6$ |
| 1024.1-c2 |
1024.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{16} \) |
$1.42974$ |
$(a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.515905150$ |
$22.83054565$ |
2.082145936 |
\( 384 a + 2432 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -1\) , \( a - 1\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}-{x}+a-1$ |
| 1024.1-c3 |
1024.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{23} \) |
$1.42974$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.031810300$ |
$5.707636413$ |
2.082145936 |
\( -274424 a + 418576 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 10 a - 21\) , \( 39 a - 61\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(10a-21\right){x}+39a-61$ |
| 1024.1-c4 |
1024.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( - 2^{23} \) |
$1.42974$ |
$(a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.031810300$ |
$11.41527282$ |
2.082145936 |
\( 1609752 a + 2278112 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -10 a - 1\) , \( 7 a + 15\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-10a-1\right){x}+7a+15$ |
| 1024.1-d1 |
1024.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( - 2^{24} \) |
$1.42974$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-32$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1.920503190$ |
$3.172496733$ |
2.154126597 |
\( -18473000 a + 26125000 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 20 a - 23\) , \( 40 a - 69\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(20a-23\right){x}+40a-69$ |
| 1024.1-d2 |
1024.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( - 2^{24} \) |
$1.42974$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-32$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.240062898$ |
$12.68998693$ |
2.154126597 |
\( -18473000 a + 26125000 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 20 a - 23\) , \( -40 a + 69\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(20a-23\right){x}-40a+69$ |
| 1024.1-d3 |
1024.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$1.42974$ |
$(a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.960251595$ |
$12.68998693$ |
2.154126597 |
\( 8000 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -3\) , \( -1\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-3{x}-1$ |
| 1024.1-d4 |
1024.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$1.42974$ |
$(a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.480125797$ |
$25.37997386$ |
2.154126597 |
\( 8000 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -3\) , \( 1\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-3{x}+1$ |
| 1024.1-d5 |
1024.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( - 2^{24} \) |
$1.42974$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-32$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1.920503190$ |
$3.172496733$ |
2.154126597 |
\( 18473000 a + 26125000 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -20 a - 23\) , \( -40 a - 69\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-20a-23\right){x}-40a-69$ |
| 1024.1-d6 |
1024.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( - 2^{24} \) |
$1.42974$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-32$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.240062898$ |
$12.68998693$ |
2.154126597 |
\( 18473000 a + 26125000 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -20 a - 23\) , \( 40 a + 69\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-20a-23\right){x}+40a+69$ |
| 1024.1-e1 |
1024.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( - 2^{23} \) |
$1.42974$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.231561135$ |
$12.35399050$ |
2.022823242 |
\( -1609752 a + 2278112 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 24 a + 32\) , \( 32 a + 48\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(24a+32\right){x}+32a+48$ |
| 1024.1-e2 |
1024.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{16} \) |
$1.42974$ |
$(a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.463122270$ |
$24.70798101$ |
2.022823242 |
\( -384 a + 2432 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 2 a - 3\) , \( -2 a + 3\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(2a-3\right){x}-2a+3$ |
| 1024.1-e3 |
1024.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( - 2^{14} \) |
$1.42974$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$0.926244540$ |
$12.35399050$ |
2.022823242 |
\( 38944 a + 56032 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -2 a + 2\) , \( -2 a + 2\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-2a+2\right){x}-2a+2$ |
| 1024.1-e4 |
1024.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{23} \) |
$1.42974$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.231561135$ |
$12.35399050$ |
2.022823242 |
\( 274424 a + 418576 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 12 a - 23\) , \( 32 a - 37\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(12a-23\right){x}+32a-37$ |
| 1024.1-f1 |
1024.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( - 2^{27} \) |
$1.42974$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-64$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$9.722981027$ |
1.718796454 |
\( -29071392966 a + 41113158120 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a - 66\) , \( 308 a + 616\bigr] \) |
${y}^2={x}^{3}+\left(-4a-66\right){x}+308a+616$ |
| 1024.1-f2 |
1024.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( - 2^{27} \) |
$1.42974$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-64$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$4$ |
\( 2^{2} \) |
$1$ |
$1.215372628$ |
1.718796454 |
\( -29071392966 a + 41113158120 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a - 66\) , \( -308 a - 616\bigr] \) |
${y}^2={x}^{3}+\left(-4a-66\right){x}-308a-616$ |
| 1024.1-f3 |
1024.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$1.42974$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$9.722981027$ |
1.718796454 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a + 6\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-4a+6\right){x}$ |
| 1024.1-f4 |
1024.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$1.42974$ |
$(a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$19.44596205$ |
1.718796454 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a - 6\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(4a-6\right){x}$ |
| 1024.1-f5 |
1024.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{24} \) |
$1.42974$ |
$(a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$4.861490513$ |
1.718796454 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -44 a - 66\) , \( -196 a - 280\bigr] \) |
${y}^2={x}^{3}+\left(-44a-66\right){x}-196a-280$ |
| 1024.1-f6 |
1024.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{24} \) |
$1.42974$ |
$(a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$19.44596205$ |
1.718796454 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -44 a - 66\) , \( 196 a + 280\bigr] \) |
${y}^2={x}^{3}+\left(-44a-66\right){x}+196a+280$ |
| 1024.1-f7 |
1024.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( - 2^{27} \) |
$1.42974$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-64$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$9.722981027$ |
1.718796454 |
\( 29071392966 a + 41113158120 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a - 66\) , \( -308 a + 616\bigr] \) |
${y}^2={x}^{3}+\left(4a-66\right){x}-308a+616$ |
| 1024.1-f8 |
1024.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( - 2^{27} \) |
$1.42974$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-64$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$4$ |
\( 2^{2} \) |
$1$ |
$1.215372628$ |
1.718796454 |
\( 29071392966 a + 41113158120 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a - 66\) , \( 308 a - 616\bigr] \) |
${y}^2={x}^{3}+\left(4a-66\right){x}+308a-616$ |
| 1024.1-g1 |
1024.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{10} \) |
$1.42974$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$15.68304578$ |
1.386198502 |
\( 128 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+{x}$ |
| 1024.1-g2 |
1024.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{25} \) |
$1.42974$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.920761445$ |
1.386198502 |
\( -36872164 a + 52151080 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 20 a - 44\) , \( 92 a - 144\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(20a-44\right){x}+92a-144$ |
| 1024.1-g3 |
1024.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{20} \) |
$1.42974$ |
$(a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$15.68304578$ |
1.386198502 |
\( 10976 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -4\) , \( 4 a\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}-4{x}+4a$ |
| 1024.1-g4 |
1024.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{25} \) |
$1.42974$ |
$(a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$15.68304578$ |
1.386198502 |
\( 36872164 a + 52151080 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -20 a - 44\) , \( 92 a + 144\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-20a-44\right){x}+92a+144$ |
| 1024.1-h1 |
1024.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{10} \) |
$1.42974$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$10.67441689$ |
0.943494071 |
\( 128 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 2\) , \( a - 2\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+2{x}+a-2$ |
| 1024.1-h2 |
1024.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{25} \) |
$1.42974$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$5.337208447$ |
0.943494071 |
\( -36872164 a + 52151080 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -30 a - 53\) , \( 105 a + 141\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-30a-53\right){x}+105a+141$ |
| 1024.1-h3 |
1024.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{20} \) |
$1.42974$ |
$(a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$10.67441689$ |
0.943494071 |
\( 10976 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -10 a - 13\) , \( -19 a - 27\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-10a-13\right){x}-19a-27$ |
| 1024.1-h4 |
1024.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{25} \) |
$1.42974$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$5.337208447$ |
0.943494071 |
\( 36872164 a + 52151080 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 30 a - 53\) , \( -105 a + 141\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(30a-53\right){x}-105a+141$ |
| 1024.1-i1 |
1024.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{10} \) |
$1.42974$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$15.68304578$ |
1.386198502 |
\( 128 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+{x}$ |
| 1024.1-i2 |
1024.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{25} \) |
$1.42974$ |
$(a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$15.68304578$ |
1.386198502 |
\( -36872164 a + 52151080 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 20 a - 44\) , \( -92 a + 144\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(20a-44\right){x}-92a+144$ |
| 1024.1-i3 |
1024.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{20} \) |
$1.42974$ |
$(a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$15.68304578$ |
1.386198502 |
\( 10976 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -4\) , \( -4 a\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}-4{x}-4a$ |
| 1024.1-i4 |
1024.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{25} \) |
$1.42974$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.920761445$ |
1.386198502 |
\( 36872164 a + 52151080 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -20 a - 44\) , \( -92 a - 144\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-20a-44\right){x}-92a-144$ |
| 1024.1-j1 |
1024.1-j |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{10} \) |
$1.42974$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$23.04181365$ |
2.036627835 |
\( 128 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2\) , \( -a + 2\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+2{x}-a+2$ |
| 1024.1-j2 |
1024.1-j |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{25} \) |
$1.42974$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$11.52090682$ |
2.036627835 |
\( -36872164 a + 52151080 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -30 a - 53\) , \( -105 a - 141\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-30a-53\right){x}-105a-141$ |
| 1024.1-j3 |
1024.1-j |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{20} \) |
$1.42974$ |
$(a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$23.04181365$ |
2.036627835 |
\( 10976 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -10 a - 13\) , \( 19 a + 27\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-10a-13\right){x}+19a+27$ |
| 1024.1-j4 |
1024.1-j |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{25} \) |
$1.42974$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$11.52090682$ |
2.036627835 |
\( 36872164 a + 52151080 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 30 a - 53\) , \( 105 a - 141\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(30a-53\right){x}+105a-141$ |
| 1024.1-k1 |
1024.1-k |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( - 2^{27} \) |
$1.42974$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-64$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$2.434836127$ |
$2.430745256$ |
2.092493851 |
\( -29071392966 a + 41113158120 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 120 a - 182\) , \( 924 a - 1232\bigr] \) |
${y}^2={x}^{3}+\left(120a-182\right){x}+924a-1232$ |
| 1024.1-k2 |
1024.1-k |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( - 2^{27} \) |
$1.42974$ |
$(a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-64$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$2.434836127$ |
$4.861490513$ |
2.092493851 |
\( -29071392966 a + 41113158120 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 120 a - 182\) , \( -924 a + 1232\bigr] \) |
${y}^2={x}^{3}+\left(120a-182\right){x}-924a+1232$ |
| 1024.1-k3 |
1024.1-k |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$1.42974$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.304354515$ |
$9.722981027$ |
2.092493851 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+2{x}$ |
| 1024.1-k4 |
1024.1-k |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$1.42974$ |
$(a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.608709031$ |
$19.44596205$ |
2.092493851 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( 0\bigr] \) |
${y}^2={x}^{3}-2{x}$ |
*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.
