| 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 |
| 1764.1-a1 |
1764.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{14} \cdot 7^{6} \) |
$2.65383$ |
$(-a+2), (a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.855262355$ |
1.619405748 |
\( \frac{4913}{1296} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -8 a + 22\) , \( -387 a + 1064\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-8a+22\right){x}-387a+1064$ |
| 1764.1-a2 |
1764.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{22} \cdot 7^{6} \) |
$2.65383$ |
$(-a+2), (a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.855262355$ |
1.619405748 |
\( \frac{838561807}{26244} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 412 a - 1238\) , \( -7107 a + 19544\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(412a-1238\right){x}-7107a+19544$ |
| 1764.1-b1 |
1764.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{6} \cdot 7^{4} \) |
$2.65383$ |
$(-a+2), (a+3), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.590274639$ |
4.637105514 |
\( -\frac{67645179}{8} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -93\) , \( -323\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-93{x}-323$ |
| 1764.1-b2 |
1764.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{18} \cdot 3^{6} \cdot 7^{4} \) |
$2.65383$ |
$(-a+2), (a+3), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$1$ |
$1.770823918$ |
4.637105514 |
\( \frac{189}{512} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -8 a + 21\) , \( 942 a - 2630\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-8a+21\right){x}+942a-2630$ |
| 1764.1-c1 |
1764.1-c |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{30} \cdot 3^{8} \cdot 7^{8} \) |
$2.65383$ |
$(-a+2), (a+3), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$4.505155042$ |
$0.472368201$ |
3.715101942 |
\( -\frac{16591834777}{98304} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( -2135 a - 4269\) , \( -88821 a - 155437\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-2135a-4269\right){x}-88821a-155437$ |
| 1764.1-c2 |
1764.1-c |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{10} \cdot 3^{12} \cdot 7^{8} \) |
$2.65383$ |
$(-a+2), (a+3), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$1.501718347$ |
$1.417104603$ |
3.715101942 |
\( \frac{596183}{864} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( 70 a + 141\) , \( -621 a - 1087\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(70a+141\right){x}-621a-1087$ |
| 1764.1-d1 |
1764.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{8} \cdot 7^{2} \) |
$2.65383$ |
$(-a+2), (a+3), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 3 \) |
$0.322661945$ |
$3.078693352$ |
5.202544171 |
\( -\frac{177017}{24} a - \frac{98239}{8} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 9\) , \( 3 a - 8\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+9{x}+3a-8$ |
| 1764.1-e1 |
1764.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{8} \cdot 7^{8} \) |
$2.65383$ |
$(-a+2), (a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.232025103$ |
$4.278162183$ |
5.198688708 |
\( -\frac{425636509}{1344} a - \frac{381284773}{672} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -62 a - 149\) , \( 293 a + 919\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-62a-149\right){x}+293a+919$ |
| 1764.1-e2 |
1764.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{10} \cdot 7^{7} \) |
$2.65383$ |
$(-a+2), (a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.464050206$ |
$4.278162183$ |
5.198688708 |
\( \frac{231911981056783}{504} a + \frac{138473755505959}{168} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -902 a - 2669\) , \( 26669 a + 61231\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-902a-2669\right){x}+26669a+61231$ |
| 1764.1-f1 |
1764.1-f |
$2$ |
$7$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{14} \cdot 3^{20} \cdot 7^{4} \) |
$2.65383$ |
$(-a+2), (a+3), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$7$ |
7B.6.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.793297333$ |
$0.882397988$ |
3.666081354 |
\( -\frac{6329617441}{279936} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 423 a - 1269\) , \( -7884 a + 21681\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(423a-1269\right){x}-7884a+21681$ |
| 1764.1-f2 |
1764.1-f |
$2$ |
$7$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{8} \cdot 7^{4} \) |
$2.65383$ |
$(-a+2), (a+3), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$7$ |
7B.6.3 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.113328190$ |
$6.176785918$ |
3.666081354 |
\( -\frac{2401}{6} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 3 a - 9\) , \( 12 a - 33\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(3a-9\right){x}+12a-33$ |
| 1764.1-g1 |
1764.1-g |
$1$ |
$1$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{8} \cdot 7^{2} \) |
$2.65383$ |
$(-a+2), (a+3), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 3 \) |
$0.062978399$ |
$12.51330712$ |
4.127293190 |
\( \frac{177017}{24} a - \frac{235867}{12} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 22 a - 50\) , \( -74 a + 219\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(22a-50\right){x}-74a+219$ |
| 1764.1-h1 |
1764.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{8} \cdot 7^{8} \) |
$2.65383$ |
$(-a+2), (a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1.667615591$ |
$0.471542841$ |
4.118306807 |
\( \frac{425636509}{1344} a - \frac{396068685}{448} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -184 a - 345\) , \( -9461 a - 16964\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-184a-345\right){x}-9461a-16964$ |
| 1764.1-h2 |
1764.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{10} \cdot 7^{7} \) |
$2.65383$ |
$(-a+2), (a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$3.335231183$ |
$0.471542841$ |
4.118306807 |
\( -\frac{231911981056783}{504} a + \frac{161833311893665}{126} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -5224 a - 9585\) , \( -322781 a - 579428\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-5224a-9585\right){x}-322781a-579428$ |
| 1764.1-i1 |
1764.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{8} \cdot 7^{8} \) |
$2.65383$ |
$(-a+2), (a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.232025103$ |
$4.278162183$ |
5.198688708 |
\( \frac{425636509}{1344} a - \frac{396068685}{448} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 65 a - 208\) , \( -440 a + 1529\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(65a-208\right){x}-440a+1529$ |
| 1764.1-i2 |
1764.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{10} \cdot 7^{7} \) |
$2.65383$ |
$(-a+2), (a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.464050206$ |
$4.278162183$ |
5.198688708 |
\( -\frac{231911981056783}{504} a + \frac{161833311893665}{126} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 905 a - 3568\) , \( -29336 a + 92417\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(905a-3568\right){x}-29336a+92417$ |
| 1764.1-j1 |
1764.1-j |
$1$ |
$1$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{8} \cdot 7^{2} \) |
$2.65383$ |
$(-a+2), (a+3), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 3 \) |
$0.322661945$ |
$3.078693352$ |
5.202544171 |
\( \frac{177017}{24} a - \frac{235867}{12} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 4 a + 2\) , \( 2 a + 1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(4a+2\right){x}+2a+1$ |
| 1764.1-k1 |
1764.1-k |
$2$ |
$7$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{14} \cdot 3^{20} \cdot 7^{4} \) |
$2.65383$ |
$(-a+2), (a+3), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$7$ |
7B.6.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.793297333$ |
$0.882397988$ |
3.666081354 |
\( -\frac{6329617441}{279936} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -423 a - 846\) , \( 7884 a + 13797\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-423a-846\right){x}+7884a+13797$ |
| 1764.1-k2 |
1764.1-k |
$2$ |
$7$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{8} \cdot 7^{4} \) |
$2.65383$ |
$(-a+2), (a+3), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$7$ |
7B.6.3 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.113328190$ |
$6.176785918$ |
3.666081354 |
\( -\frac{2401}{6} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -3 a - 6\) , \( -12 a - 21\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-3a-6\right){x}-12a-21$ |
| 1764.1-l1 |
1764.1-l |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{8} \cdot 7^{8} \) |
$2.65383$ |
$(-a+2), (a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1.667615591$ |
$0.471542841$ |
4.118306807 |
\( -\frac{425636509}{1344} a - \frac{381284773}{672} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 188 a - 526\) , \( 9119 a - 25496\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(188a-526\right){x}+9119a-25496$ |
| 1764.1-l2 |
1764.1-l |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{10} \cdot 7^{7} \) |
$2.65383$ |
$(-a+2), (a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$3.335231183$ |
$0.471542841$ |
4.118306807 |
\( \frac{231911981056783}{504} a + \frac{138473755505959}{168} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 5228 a - 14806\) , \( 313199 a - 876080\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(5228a-14806\right){x}+313199a-876080$ |
| 1764.1-m1 |
1764.1-m |
$1$ |
$1$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{8} \cdot 7^{2} \) |
$2.65383$ |
$(-a+2), (a+3), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 3 \) |
$0.062978399$ |
$12.51330712$ |
4.127293190 |
\( -\frac{177017}{24} a - \frac{98239}{8} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -19 a - 34\) , \( 42 a + 75\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-19a-34\right){x}+42a+75$ |
| 1764.1-n1 |
1764.1-n |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{30} \cdot 3^{8} \cdot 7^{8} \) |
$2.65383$ |
$(-a+2), (a+3), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$4.505155042$ |
$0.472368201$ |
3.715101942 |
\( -\frac{16591834777}{98304} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 2134 a - 6404\) , \( 88821 a - 244258\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2134a-6404\right){x}+88821a-244258$ |
| 1764.1-n2 |
1764.1-n |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{10} \cdot 3^{12} \cdot 7^{8} \) |
$2.65383$ |
$(-a+2), (a+3), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$1.501718347$ |
$1.417104603$ |
3.715101942 |
\( \frac{596183}{864} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -71 a + 211\) , \( 621 a - 1708\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-71a+211\right){x}+621a-1708$ |
| 1764.1-o1 |
1764.1-o |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{6} \cdot 7^{4} \) |
$2.65383$ |
$(-a+2), (a+3), (2)$ |
$2$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.087955346$ |
$15.21595931$ |
4.672743225 |
\( -\frac{67645179}{8} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 465 a - 1302\) , \( -7752 a + 21641\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(465a-1302\right){x}-7752a+21641$ |
| 1764.1-o2 |
1764.1-o |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{18} \cdot 3^{6} \cdot 7^{4} \) |
$2.65383$ |
$(-a+2), (a+3), (2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$0.009772816$ |
$5.071986438$ |
4.672743225 |
\( \frac{189}{512} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 1\) , \( 39\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+{x}+39$ |
| 1764.1-p1 |
1764.1-p |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{14} \cdot 7^{6} \) |
$2.65383$ |
$(-a+2), (a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.855262355$ |
1.619405748 |
\( \frac{4913}{1296} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( 7 a + 15\) , \( 387 a + 677\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(7a+15\right){x}+387a+677$ |
| 1764.1-p2 |
1764.1-p |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1764.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{22} \cdot 7^{6} \) |
$2.65383$ |
$(-a+2), (a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.855262355$ |
1.619405748 |
\( \frac{838561807}{26244} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( -413 a - 825\) , \( 7107 a + 12437\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-413a-825\right){x}+7107a+12437$ |
*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.
