| 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 |
| 576.1-a1 |
576.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{8} \cdot 3^{13} \) |
$2.00611$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$9.800884644$ |
2.138728369 |
\( -\frac{25019564800}{81} a + \frac{69836807168}{81} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 23 a - 61\) , \( -58 a + 268\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(23a-61\right){x}-58a+268$ |
| 576.1-a2 |
576.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{20} \) |
$2.00611$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.900442322$ |
2.138728369 |
\( \frac{11855696}{2187} a + \frac{35052272}{729} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -52 a - 196\) , \( 548 a + 1348\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-52a-196\right){x}+548a+1348$ |
| 576.1-b1 |
576.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{8} \cdot 3^{7} \) |
$2.00611$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.556897496$ |
$14.09410213$ |
3.425571431 |
\( \frac{256}{3} a + \frac{4864}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+3{x}$ |
| 576.1-b2 |
576.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{8} \) |
$2.00611$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.278448748$ |
$7.047051066$ |
3.425571431 |
\( \frac{77872}{3} a + \frac{145568}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -12\) , \( -12 a - 12\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-12{x}-12a-12$ |
| 576.1-c1 |
576.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{22} \) |
$2.00611$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$7.063080417$ |
$1.049434289$ |
3.234966217 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -46 a + 143\) , \( 2113 a - 5797\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-46a+143\right){x}+2113a-5797$ |
| 576.1-c2 |
576.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \) |
$2.00611$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.882885052$ |
$8.395474317$ |
3.234966217 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -a + 8\) , \( -2 a + 8\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-a+8\right){x}-2a+8$ |
| 576.1-c3 |
576.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{10} \) |
$2.00611$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.765770104$ |
$8.395474317$ |
3.234966217 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 14 a - 37\) , \( -35 a + 95\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(14a-37\right){x}-35a+95$ |
| 576.1-c4 |
576.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{14} \) |
$2.00611$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$3.531540208$ |
$4.197737158$ |
3.234966217 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 74 a - 217\) , \( 505 a - 1405\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(74a-217\right){x}+505a-1405$ |
| 576.1-c5 |
576.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{8} \) |
$2.00611$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.882885052$ |
$4.197737158$ |
3.234966217 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 194 a - 577\) , \( -2447 a + 6683\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(194a-577\right){x}-2447a+6683$ |
| 576.1-c6 |
576.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{10} \) |
$2.00611$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$7.063080417$ |
$2.098868579$ |
3.234966217 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 1154 a - 3457\) , \( 34417 a - 94933\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(1154a-3457\right){x}+34417a-94933$ |
| 576.1-d1 |
576.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{20} \) |
$2.00611$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.662960981$ |
0.725775673 |
\( -\frac{11855696}{2187} a + \frac{117012512}{2187} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -512 a - 932\) , \( -8788 a - 15768\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-512a-932\right){x}-8788a-15768$ |
| 576.1-d2 |
576.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{8} \cdot 3^{13} \) |
$2.00611$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.662960981$ |
0.725775673 |
\( \frac{25019564800}{81} a + \frac{44817242368}{81} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 8 a - 22\) , \( 2549 a - 7115\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(8a-22\right){x}+2549a-7115$ |
| 576.1-e1 |
576.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{8} \cdot 3^{7} \) |
$2.00611$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.556897496$ |
$14.09410213$ |
3.425571431 |
\( -\frac{256}{3} a + \frac{5120}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 2 a + 2\) , \( -a - 2\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a+2\right){x}-a-2$ |
| 576.1-e2 |
576.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{8} \) |
$2.00611$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.278448748$ |
$7.047051066$ |
3.425571431 |
\( -\frac{77872}{3} a + 74480 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 2 a - 13\) , \( 11 a - 11\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a-13\right){x}+11a-11$ |
| 576.1-f1 |
576.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{8} \cdot 3^{7} \) |
$2.00611$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.256205592$ |
$11.80120592$ |
2.639157676 |
\( -\frac{256}{3} a + \frac{5120}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 10 a - 23\) , \( 4 a - 9\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(10a-23\right){x}+4a-9$ |
| 576.1-f2 |
576.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{8} \) |
$2.00611$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.128102796$ |
$11.80120592$ |
2.639157676 |
\( -\frac{77872}{3} a + 74480 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -60 a - 108\) , \( -228 a - 408\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-60a-108\right){x}-228a-408$ |
| 576.1-g1 |
576.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{20} \) |
$2.00611$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.900442322$ |
2.138728369 |
\( -\frac{11855696}{2187} a + \frac{117012512}{2187} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 54 a - 249\) , \( -495 a + 1647\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(54a-249\right){x}-495a+1647$ |
| 576.1-g2 |
576.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{8} \cdot 3^{13} \) |
$2.00611$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$9.800884644$ |
2.138728369 |
\( \frac{25019564800}{81} a + \frac{44817242368}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -21 a - 39\) , \( 36 a + 171\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-21a-39\right){x}+36a+171$ |
| 576.1-h1 |
576.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{20} \cdot 3^{7} \) |
$2.00611$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$7.143783228$ |
3.117802608 |
\( -\frac{5202690124}{3} a + \frac{14522206328}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 41 a + 23\) , \( 355 a + 788\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(41a+23\right){x}+355a+788$ |
| 576.1-h2 |
576.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{8} \cdot 3^{7} \) |
$2.00611$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$14.28756645$ |
3.117802608 |
\( \frac{4864}{3} a + \frac{8704}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -4 a - 7\) , \( -14 a - 25\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-4a-7\right){x}-14a-25$ |
| 576.1-h3 |
576.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{8} \) |
$2.00611$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$14.28756645$ |
3.117802608 |
\( -\frac{53200}{3} a + 58128 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -19 a - 37\) , \( 43 a + 80\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-19a-37\right){x}+43a+80$ |
| 576.1-h4 |
576.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{10} \) |
$2.00611$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$7.143783228$ |
3.117802608 |
\( \frac{121322980}{9} a + \frac{217342184}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -319 a - 577\) , \( 4339 a + 7772\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-319a-577\right){x}+4339a+7772$ |
| 576.1-i1 |
576.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{8} \cdot 3^{7} \) |
$2.00611$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.256205592$ |
$11.80120592$ |
2.639157676 |
\( \frac{256}{3} a + \frac{4864}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -8 a - 14\) , \( 5 a + 9\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-8a-14\right){x}+5a+9$ |
| 576.1-i2 |
576.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{8} \) |
$2.00611$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.128102796$ |
$11.80120592$ |
2.639157676 |
\( \frac{77872}{3} a + \frac{145568}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 62 a - 169\) , \( 167 a - 467\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(62a-169\right){x}+167a-467$ |
| 576.1-j1 |
576.1-j |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{8} \cdot 3^{7} \) |
$2.00611$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$14.28756645$ |
3.117802608 |
\( -\frac{4864}{3} a + \frac{13568}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 6 a - 12\) , \( 9 a - 27\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(6a-12\right){x}+9a-27$ |
| 576.1-j2 |
576.1-j |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{10} \) |
$2.00611$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$7.143783228$ |
3.117802608 |
\( -\frac{121322980}{9} a + \frac{112888388}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 321 a - 897\) , \( -4659 a + 13008\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(321a-897\right){x}-4659a+13008$ |
| 576.1-j3 |
576.1-j |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{8} \) |
$2.00611$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$14.28756645$ |
3.117802608 |
\( \frac{53200}{3} a + \frac{121184}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 21 a - 57\) , \( -63 a + 180\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(21a-57\right){x}-63a+180$ |
| 576.1-j4 |
576.1-j |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{20} \cdot 3^{7} \) |
$2.00611$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$7.143783228$ |
3.117802608 |
\( \frac{5202690124}{3} a + \frac{9319516204}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -39 a + 63\) , \( -315 a + 1080\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-39a+63\right){x}-315a+1080$ |
| 576.1-k1 |
576.1-k |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{22} \) |
$2.00611$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$7.063080417$ |
$1.049434289$ |
3.234966217 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 48 a + 96\) , \( -2160 a - 3780\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(48a+96\right){x}-2160a-3780$ |
| 576.1-k2 |
576.1-k |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \) |
$2.00611$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.882885052$ |
$8.395474317$ |
3.234966217 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 3 a + 6\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(3a+6\right){x}$ |
| 576.1-k3 |
576.1-k |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{10} \) |
$2.00611$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.765770104$ |
$8.395474317$ |
3.234966217 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -12 a - 24\) , \( 48 a + 84\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-12a-24\right){x}+48a+84$ |
| 576.1-k4 |
576.1-k |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{14} \) |
$2.00611$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$3.531540208$ |
$4.197737158$ |
3.234966217 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -72 a - 144\) , \( -432 a - 756\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-72a-144\right){x}-432a-756$ |
| 576.1-k5 |
576.1-k |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{8} \) |
$2.00611$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.882885052$ |
$4.197737158$ |
3.234966217 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -192 a - 384\) , \( 2640 a + 4620\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-192a-384\right){x}+2640a+4620$ |
| 576.1-k6 |
576.1-k |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{10} \) |
$2.00611$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$7.063080417$ |
$2.098868579$ |
3.234966217 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -1152 a - 2304\) , \( -33264 a - 58212\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1152a-2304\right){x}-33264a-58212$ |
| 576.1-l1 |
576.1-l |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{8} \cdot 3^{13} \) |
$2.00611$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.662960981$ |
0.725775673 |
\( -\frac{25019564800}{81} a + \frac{69836807168}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -6 a - 15\) , \( -2556 a - 4581\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-6a-15\right){x}-2556a-4581$ |
| 576.1-l2 |
576.1-l |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{20} \) |
$2.00611$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.662960981$ |
0.725775673 |
\( \frac{11855696}{2187} a + \frac{35052272}{729} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 514 a - 1445\) , \( 9301 a - 26001\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(514a-1445\right){x}+9301a-26001$ |
| 576.1-m1 |
576.1-m |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{8} \cdot 3^{7} \) |
$2.00611$ |
$(-a+2), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$11.03440239$ |
1.203952004 |
\( -\frac{4864}{3} a + \frac{13568}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 1\) , \( -2 a - 3\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+1\right){x}-2a-3$ |
| 576.1-m2 |
576.1-m |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{10} \) |
$2.00611$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.758600597$ |
1.203952004 |
\( -\frac{121322980}{9} a + \frac{112888388}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -14 a - 89\) , \( 49 a - 93\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-14a-89\right){x}+49a-93$ |
| 576.1-m3 |
576.1-m |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{8} \) |
$2.00611$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$5.517201195$ |
1.203952004 |
\( \frac{53200}{3} a + \frac{121184}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -14 a - 29\) , \( -71 a - 129\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-14a-29\right){x}-71a-129$ |
| 576.1-m4 |
576.1-m |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{20} \cdot 3^{7} \) |
$2.00611$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.379300298$ |
1.203952004 |
\( \frac{5202690124}{3} a + \frac{9319516204}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -254 a - 449\) , \( -3647 a - 6549\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-254a-449\right){x}-3647a-6549$ |
| 576.1-n1 |
576.1-n |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{20} \cdot 3^{7} \) |
$2.00611$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.379300298$ |
1.203952004 |
\( -\frac{5202690124}{3} a + \frac{14522206328}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 256 a - 704\) , \( 3392 a - 9492\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(256a-704\right){x}+3392a-9492$ |
| 576.1-n2 |
576.1-n |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{8} \cdot 3^{7} \) |
$2.00611$ |
$(-a+2), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$11.03440239$ |
1.203952004 |
\( \frac{4864}{3} a + \frac{8704}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 1\) , \( 2 a - 6\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+1\right){x}+2a-6$ |
| 576.1-n3 |
576.1-n |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{8} \) |
$2.00611$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$5.517201195$ |
1.203952004 |
\( -\frac{53200}{3} a + 58128 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 16 a - 44\) , \( 56 a - 156\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(16a-44\right){x}+56a-156$ |
| 576.1-n4 |
576.1-n |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{10} \) |
$2.00611$ |
$(-a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.758600597$ |
1.203952004 |
\( \frac{121322980}{9} a + \frac{217342184}{9} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 16 a - 104\) , \( -64 a + 60\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(16a-104\right){x}-64a+60$ |
*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.
