| 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 |
| 256.1-a1 |
256.1-a |
$4$ |
$21$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{28} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 7$ |
3B, 7B.6.3 |
$1$ |
\( 2^{4} \) |
$1$ |
$1.915537937$ |
4.059507167 |
\( -\frac{293180476215589246298781}{8} a - \frac{960141789432972248487021}{8} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -10282063 a - 33672998\) , \( 34886965210 a + 114251923320\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-10282063a-33672998\right){x}+34886965210a+114251923320$ |
| 256.1-a2 |
256.1-a |
$4$ |
$21$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{28} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 7$ |
3B, 7B.6.3 |
$1$ |
\( 2^{4} \) |
$1$ |
$1.915537937$ |
4.059507167 |
\( \frac{293180476215589246298781}{8} a - \frac{626661132824280747392901}{4} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 10282065 a - 43955062\) , \( -34876683146 a + 149094933468\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(10282065a-43955062\right){x}-34876683146a+149094933468$ |
| 256.1-a3 |
256.1-a |
$4$ |
$21$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{52} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 7$ |
3B, 7B.6.1 |
$1$ |
\( 2^{4} \) |
$1$ |
$1.915537937$ |
4.059507167 |
\( -\frac{699691689}{2097152} a - \frac{307208349}{2097152} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -3823 a - 12518\) , \( 369018 a + 1208504\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3823a-12518\right){x}+369018a+1208504$ |
| 256.1-a4 |
256.1-a |
$4$ |
$21$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{52} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 7$ |
3B, 7B.6.1 |
$1$ |
\( 2^{4} \) |
$1$ |
$1.915537937$ |
4.059507167 |
\( \frac{699691689}{2097152} a - \frac{503450019}{1048576} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 3825 a - 16342\) , \( -365194 a + 1561180\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(3825a-16342\right){x}-365194a+1561180$ |
| 256.1-b1 |
256.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{33} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.349961086$ |
$2.170376093$ |
2.702204615 |
\( -\frac{7754659}{1024} a + \frac{9383969}{512} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 44320 a - 189464\) , \( 9682784 a - 41393100\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(44320a-189464\right){x}+9682784a-41393100$ |
| 256.1-b2 |
256.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{27} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.174980543$ |
$2.170376093$ |
2.702204615 |
\( \frac{925430099}{32} a + \frac{1515353487}{16} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -3 a + 10\) , \( 204 a - 884\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-3a+10\right){x}+204a-884$ |
| 256.1-c1 |
256.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{33} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{3} \) |
$1$ |
$0.789181095$ |
1.881532613 |
\( -\frac{20297286875}{64} a + \frac{43383068421}{32} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 1461 a - 6246\) , \( 57028 a - 243796\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(1461a-6246\right){x}+57028a-243796$ |
| 256.1-c2 |
256.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{27} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$7.102629859$ |
1.881532613 |
\( -\frac{489}{4} a + 1841 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 21 a - 86\) , \( 20 a - 84\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(21a-86\right){x}+20a-84$ |
| 256.1-c3 |
256.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{27} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$7.102629859$ |
1.881532613 |
\( \frac{489}{4} a + \frac{6875}{4} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -21 a - 65\) , \( -20 a - 64\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-21a-65\right){x}-20a-64$ |
| 256.1-c4 |
256.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{33} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{3} \) |
$1$ |
$0.789181095$ |
1.881532613 |
\( \frac{20297286875}{64} a + \frac{66468849967}{64} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -1461 a - 4785\) , \( -57028 a - 186768\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-1461a-4785\right){x}-57028a-186768$ |
| 256.1-d1 |
256.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{24} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{3} \) |
$0.270502588$ |
$3.783765348$ |
2.169093018 |
\( -\frac{4171}{2} a - 5149 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -21 a - 65\) , \( -140 a - 460\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-21a-65\right){x}-140a-460$ |
| 256.1-e1 |
256.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{20} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.523959333$ |
$20.62619196$ |
2.862919944 |
\( 7168 a - 30720 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 2823 a - 12062\) , \( -158029 a + 675558\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(2823a-12062\right){x}-158029a+675558$ |
| 256.1-f1 |
256.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{24} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{3} \) |
$0.270502588$ |
$3.783765348$ |
2.169093018 |
\( \frac{4171}{2} a - \frac{14469}{2} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 21 a - 86\) , \( 140 a - 600\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(21a-86\right){x}+140a-600$ |
| 256.1-g1 |
256.1-g |
$1$ |
$1$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{20} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.523959333$ |
$20.62619196$ |
2.862919944 |
\( -7168 a - 23552 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -2823 a - 9239\) , \( 158029 a + 517529\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-2823a-9239\right){x}+158029a+517529$ |
| 256.1-h1 |
256.1-h |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{8} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2, 19$ |
2B, 19Ns.2.1 |
$1$ |
\( 1 \) |
$1$ |
$17.69503190$ |
0.585941058 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 5\) , \( 133 a + 436\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+5\right){x}+133a+436$ |
| 256.1-h2 |
256.1-h |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{8} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2, 19$ |
2B, 19Ns.2.1 |
$1$ |
\( 1 \) |
$1$ |
$17.69503190$ |
0.585941058 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 5\) , \( -133 a + 574\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+5\right){x}-133a+574$ |
| 256.1-h3 |
256.1-h |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{16} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$19$ |
19Ns.2.1 |
$1$ |
\( 1 \) |
$1$ |
$17.69503190$ |
0.585941058 |
\( 54000 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -199 a - 650\) , \( 3294 a + 10788\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-199a-650\right){x}+3294a+10788$ |
| 256.1-h4 |
256.1-h |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{16} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$19$ |
19Ns.2.1 |
$1$ |
\( 1 \) |
$1$ |
$17.69503190$ |
0.585941058 |
\( 54000 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 201 a - 850\) , \( -3094 a + 13232\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(201a-850\right){x}-3094a+13232$ |
| 256.1-i1 |
256.1-i |
$2$ |
$3$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{20} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$19$ |
19Ns.2.1 |
$1$ |
\( 2 \) |
$1$ |
$8.847515954$ |
2.343764232 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 5\) , \( 93 a - 403\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+5\right){x}+93a-403$ |
| 256.1-i2 |
256.1-i |
$2$ |
$3$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{20} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$19$ |
19Ns.2.1 |
$1$ |
\( 2 \) |
$1$ |
$8.847515954$ |
2.343764232 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 5\) , \( -12213 a - 39997\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+5\right){x}-12213a-39997$ |
| 256.1-j1 |
256.1-j |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{27} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.174980543$ |
$2.170376093$ |
2.702204615 |
\( -\frac{925430099}{32} a + \frac{3956137073}{32} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 3 a + 7\) , \( -204 a - 680\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(3a+7\right){x}-204a-680$ |
| 256.1-j2 |
256.1-j |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{33} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.349961086$ |
$2.170376093$ |
2.702204615 |
\( \frac{7754659}{1024} a + \frac{11013279}{1024} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -44320 a - 145144\) , \( -9682784 a - 31710316\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-44320a-145144\right){x}-9682784a-31710316$ |
| 256.1-k1 |
256.1-k |
$1$ |
$1$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{24} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{3} \) |
$0.156656317$ |
$11.06868076$ |
3.674737569 |
\( \frac{4171}{2} a - \frac{14469}{2} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 2395 a + 7847\) , \( -24172 a - 79160\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(2395a+7847\right){x}-24172a-79160$ |
| 256.1-l1 |
256.1-l |
$2$ |
$3$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{20} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$19$ |
19Ns.2.1 |
$1$ |
\( 2 \) |
$1$ |
$8.847515954$ |
2.343764232 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 5\) , \( 12213 a - 52215\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+5\right){x}+12213a-52215$ |
| 256.1-l2 |
256.1-l |
$2$ |
$3$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{20} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$19$ |
19Ns.2.1 |
$1$ |
\( 2 \) |
$1$ |
$8.847515954$ |
2.343764232 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 5\) , \( -93 a - 305\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+5\right){x}-93a-305$ |
| 256.1-m1 |
256.1-m |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{27} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.979895166$ |
$11.24713795$ |
5.839076984 |
\( -\frac{925430099}{32} a + \frac{3956137073}{32} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 77309 a - 330486\) , \( -22623164 a + 96712152\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(77309a-330486\right){x}-22623164a+96712152$ |
| 256.1-m2 |
256.1-m |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{33} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.489947583$ |
$11.24713795$ |
5.839076984 |
\( \frac{7754659}{1024} a + \frac{11013279}{1024} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 27 a - 113\) , \( -188 a + 804\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(27a-113\right){x}-188a+804$ |
| 256.1-n1 |
256.1-n |
$1$ |
$1$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{20} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$7.564554459$ |
$2.988785561$ |
5.989225681 |
\( -7168 a - 23552 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 4 a - 17\) , \( 40 a - 171\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(4a-17\right){x}+40a-171$ |
| 256.1-o1 |
256.1-o |
$1$ |
$1$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{20} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$7.564554459$ |
$2.988785561$ |
5.989225681 |
\( 7168 a - 30720 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -4 a - 13\) , \( -40 a - 131\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-4a-13\right){x}-40a-131$ |
| 256.1-p1 |
256.1-p |
$1$ |
$1$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{24} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{3} \) |
$0.156656317$ |
$11.06868076$ |
3.674737569 |
\( -\frac{4171}{2} a - 5149 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -2395 a + 10242\) , \( 24172 a - 103332\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-2395a+10242\right){x}+24172a-103332$ |
| 256.1-q1 |
256.1-q |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{33} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.489947583$ |
$11.24713795$ |
5.839076984 |
\( -\frac{7754659}{1024} a + \frac{9383969}{512} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -27 a - 86\) , \( 188 a + 616\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-27a-86\right){x}+188a+616$ |
| 256.1-q2 |
256.1-q |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{27} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.979895166$ |
$11.24713795$ |
5.839076984 |
\( \frac{925430099}{32} a + \frac{1515353487}{16} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -77309 a - 253177\) , \( 22623164 a + 74088988\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-77309a-253177\right){x}+22623164a+74088988$ |
| 256.1-r1 |
256.1-r |
$4$ |
$21$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{28} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 7$ |
3B, 7B.6.3 |
$49$ |
\( 2^{2} \) |
$1$ |
$0.019466671$ |
0.505371038 |
\( -\frac{293180476215589246298781}{8} a - \frac{960141789432972248487021}{8} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 1142337 a - 4884238\) , \( 1290582430 a - 5517144100\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(1142337a-4884238\right){x}+1290582430a-5517144100$ |
| 256.1-r2 |
256.1-r |
$4$ |
$21$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{28} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 7$ |
3B, 7B.6.3 |
$49$ |
\( 2^{2} \) |
$1$ |
$0.019466671$ |
0.505371038 |
\( \frac{293180476215589246298781}{8} a - \frac{626661132824280747392901}{4} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -1142335 a - 3741902\) , \( -1289440094 a - 4222819768\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1142335a-3741902\right){x}-1289440094a-4222819768$ |
| 256.1-r3 |
256.1-r |
$4$ |
$21$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{52} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 7$ |
3B, 7B.6.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$0.953866916$ |
0.505371038 |
\( -\frac{699691689}{2097152} a - \frac{307208349}{2097152} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -3423 a + 14642\) , \( -190018 a + 812316\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-3423a+14642\right){x}-190018a+812316$ |
| 256.1-r4 |
256.1-r |
$4$ |
$21$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{52} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 7$ |
3B, 7B.6.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$0.953866916$ |
0.505371038 |
\( \frac{699691689}{2097152} a - \frac{503450019}{1048576} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 3425 a + 11218\) , \( 186594 a + 611080\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(3425a+11218\right){x}+186594a+611080$ |
| 256.1-s1 |
256.1-s |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{33} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$9.323493311$ |
4.939707428 |
\( -\frac{20297286875}{64} a + \frac{43383068421}{32} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -47365 a - 155113\) , \( 11028284 a + 36116716\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-47365a-155113\right){x}+11028284a+36116716$ |
| 256.1-s2 |
256.1-s |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{27} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$9.323493311$ |
4.939707428 |
\( -\frac{489}{4} a + 1841 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 2395 a + 7847\) , \( 72492 a + 237404\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(2395a+7847\right){x}+72492a+237404$ |
| 256.1-s3 |
256.1-s |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{27} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$9.323493311$ |
4.939707428 |
\( \frac{489}{4} a + \frac{6875}{4} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -2395 a + 10242\) , \( -72492 a + 309896\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2395a+10242\right){x}-72492a+309896$ |
| 256.1-s4 |
256.1-s |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{33} \) |
$2.69858$ |
$(a-4), (a+3)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$9.323493311$ |
4.939707428 |
\( \frac{20297286875}{64} a + \frac{66468849967}{64} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 47365 a - 202478\) , \( -11028284 a + 47145000\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(47365a-202478\right){x}-11028284a+47145000$ |
*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.
