| 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 |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{12} \) |
$2.31645$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$13.75037163$ |
1.500288544 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -a + 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a+3\right){x}$ |
| 1024.1-a2 |
1024.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{24} \) |
$2.31645$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$13.75037163$ |
1.500288544 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a - 12\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(4a-12\right){x}$ |
| 1024.1-b1 |
1024.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{12} \) |
$2.31645$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$10.22133429$ |
1.115239002 |
\( -448 a - 512 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -3 a - 5\) , \( -5 a - 9\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-3a-5\right){x}-5a-9$ |
| 1024.1-b2 |
1024.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$2.31645$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$10.22133429$ |
1.115239002 |
\( 1286152 a + 2310888 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 45 a - 125\) , \( -177 a + 494\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(45a-125\right){x}-177a+494$ |
| 1024.1-c1 |
1024.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{12} \) |
$2.31645$ |
$(2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.374753435$ |
$18.23438895$ |
2.982340216 |
\( -448 a - 512 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -3 a - 5\) , \( 5 a + 9\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-3a-5\right){x}+5a+9$ |
| 1024.1-c2 |
1024.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$2.31645$ |
$(2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.374753435$ |
$18.23438895$ |
2.982340216 |
\( 1286152 a + 2310888 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 45 a - 125\) , \( 177 a - 494\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(45a-125\right){x}+177a-494$ |
| 1024.1-d1 |
1024.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{12} \) |
$2.31645$ |
$(2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1.661457220$ |
$27.50074327$ |
2.492665234 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}$ |
| 1024.1-d2 |
1024.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{24} \) |
$2.31645$ |
$(2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$3.322914441$ |
$6.875185818$ |
2.492665234 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4\) , \( 0\bigr] \) |
${y}^2={x}^{3}+4{x}$ |
| 1024.1-d3 |
1024.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$2.31645$ |
$(2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 1 \) |
$3.322914441$ |
$6.875185818$ |
2.492665234 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -11\) , \( -14\bigr] \) |
${y}^2={x}^{3}-11{x}-14$ |
| 1024.1-d4 |
1024.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$2.31645$ |
$(2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.830728610$ |
$27.50074327$ |
2.492665234 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -11\) , \( 14\bigr] \) |
${y}^2={x}^{3}-11{x}+14$ |
| 1024.1-e1 |
1024.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{12} \) |
$2.31645$ |
$(2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2 \) |
$3.286579589$ |
$7.094113679$ |
5.087830682 |
\( -64 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 1\) , \( a - 3\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+{x}+a-3$ |
| 1024.1-e2 |
1024.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$2.31645$ |
$(2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3Nn |
$1$ |
\( 1 \) |
$6.573159178$ |
$7.094113679$ |
5.087830682 |
\( 238328 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 10 a - 29\) , \( 39 a - 109\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(10a-29\right){x}+39a-109$ |
| 1024.1-f1 |
1024.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{12} \) |
$2.31645$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$10.22133429$ |
4.460956011 |
\( 448 a - 960 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+2{x}$ |
| 1024.1-f2 |
1024.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$2.31645$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$10.22133429$ |
4.460956011 |
\( -1286152 a + 3597040 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -8\) , \( 8 a - 8\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}-8{x}+8a-8$ |
| 1024.1-g1 |
1024.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{12} \) |
$2.31645$ |
$(2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2 \) |
$0.407799987$ |
$27.53331622$ |
2.450169241 |
\( -64 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 1\) , \( -a + 3\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+{x}-a+3$ |
| 1024.1-g2 |
1024.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$2.31645$ |
$(2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3Nn |
$1$ |
\( 1 \) |
$0.815599975$ |
$27.53331622$ |
2.450169241 |
\( 238328 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 10 a - 29\) , \( -39 a + 109\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(10a-29\right){x}-39a+109$ |
| 1024.1-h1 |
1024.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{12} \) |
$2.31645$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$18.23438895$ |
1.989534943 |
\( 448 a - 960 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+2{x}$ |
| 1024.1-h2 |
1024.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$2.31645$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$18.23438895$ |
1.989534943 |
\( -1286152 a + 3597040 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -8\) , \( -8 a + 8\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}-8{x}-8a+8$ |
| 1024.1-i1 |
1024.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{12} \) |
$2.31645$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$10.22133429$ |
1.115239002 |
\( 448 a - 960 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 3 a - 8\) , \( 5 a - 14\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(3a-8\right){x}+5a-14$ |
| 1024.1-i2 |
1024.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$2.31645$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$10.22133429$ |
1.115239002 |
\( -1286152 a + 3597040 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -45 a - 80\) , \( 177 a + 317\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-45a-80\right){x}+177a+317$ |
| 1024.1-j1 |
1024.1-j |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{12} \) |
$2.31645$ |
$(2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2 \) |
$3.286579589$ |
$7.094113679$ |
5.087830682 |
\( -64 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 1\) , \( -a - 2\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+{x}-a-2$ |
| 1024.1-j2 |
1024.1-j |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$2.31645$ |
$(2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3Nn |
$1$ |
\( 1 \) |
$6.573159178$ |
$7.094113679$ |
5.087830682 |
\( 238328 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -10 a - 19\) , \( -39 a - 70\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-10a-19\right){x}-39a-70$ |
| 1024.1-k1 |
1024.1-k |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{12} \) |
$2.31645$ |
$(2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.374753435$ |
$18.23438895$ |
2.982340216 |
\( 448 a - 960 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 3 a - 8\) , \( -5 a + 14\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(3a-8\right){x}-5a+14$ |
| 1024.1-k2 |
1024.1-k |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$2.31645$ |
$(2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.374753435$ |
$18.23438895$ |
2.982340216 |
\( -1286152 a + 3597040 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -45 a - 80\) , \( -177 a - 317\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-45a-80\right){x}-177a-317$ |
| 1024.1-l1 |
1024.1-l |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{12} \) |
$2.31645$ |
$(2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2 \) |
$0.407799987$ |
$27.53331622$ |
2.450169241 |
\( -64 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 1\) , \( a + 2\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+{x}+a+2$ |
| 1024.1-l2 |
1024.1-l |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$2.31645$ |
$(2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3Nn |
$1$ |
\( 1 \) |
$0.815599975$ |
$27.53331622$ |
2.450169241 |
\( 238328 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -10 a - 19\) , \( 39 a + 70\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-10a-19\right){x}+39a+70$ |
| 1024.1-m1 |
1024.1-m |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{12} \) |
$2.31645$ |
$(2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$2.988881507$ |
$27.50074327$ |
4.484184685 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 5 a - 14\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(5a-14\right){x}$ |
| 1024.1-m2 |
1024.1-m |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{24} \) |
$2.31645$ |
$(2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1.494440753$ |
$6.875185818$ |
4.484184685 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -20 a + 56\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-20a+56\right){x}$ |
| 1024.1-m3 |
1024.1-m |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$2.31645$ |
$(2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 1 \) |
$1.494440753$ |
$27.50074327$ |
4.484184685 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 55 a - 154\) , \( -336 a + 938\bigr] \) |
${y}^2={x}^{3}+\left(55a-154\right){x}-336a+938$ |
| 1024.1-m4 |
1024.1-m |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$2.31645$ |
$(2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1.494440753$ |
$6.875185818$ |
4.484184685 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 55 a - 154\) , \( 336 a - 938\bigr] \) |
${y}^2={x}^{3}+\left(55a-154\right){x}+336a-938$ |
| 1024.1-n1 |
1024.1-n |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{12} \) |
$2.31645$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$10.22133429$ |
4.460956011 |
\( -448 a - 512 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+2{x}$ |
| 1024.1-n2 |
1024.1-n |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$2.31645$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$10.22133429$ |
4.460956011 |
\( 1286152 a + 2310888 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -8\) , \( -8 a\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}-8{x}-8a$ |
| 1024.1-o1 |
1024.1-o |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{12} \) |
$2.31645$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$18.23438895$ |
1.989534943 |
\( -448 a - 512 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+2{x}$ |
| 1024.1-o2 |
1024.1-o |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$2.31645$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$18.23438895$ |
1.989534943 |
\( 1286152 a + 2310888 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -8\) , \( 8 a\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}-8{x}+8a$ |
| 1024.1-p1 |
1024.1-p |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{12} \) |
$2.31645$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$13.75037163$ |
1.500288544 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( a + 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a+2\right){x}$ |
| 1024.1-p2 |
1024.1-p |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{24} \) |
$2.31645$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$13.75037163$ |
1.500288544 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a - 8\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-4a-8\right){x}$ |
*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.
