| 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 |
| 1.1-a1 |
1.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.78412$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$11$ |
11Ns.3.1 |
$1$ |
\( 1 \) |
$1$ |
$26.16385905$ |
0.745412115 |
\( -3375 \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -2 a + 7\) , \( -a + 7\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a+7\right){x}-a+7$ |
| 1.1-a2 |
1.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.78412$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$11$ |
11Ns.3.1 |
$1$ |
\( 1 \) |
$1$ |
$26.16385905$ |
0.745412115 |
\( -3375 \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 2 a + 4\) , \( 3 a + 10\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(2a+4\right){x}+3a+10$ |
| 1.1-a3 |
1.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.78412$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$11$ |
11Ns.3.1 |
$1$ |
\( 1 \) |
$1$ |
$26.16385905$ |
0.745412115 |
\( 16581375 \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -7 a - 13\) , \( 13 a + 60\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-7a-13\right){x}+13a+60$ |
| 1.1-a4 |
1.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.78412$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$11$ |
11Ns.3.1 |
$1$ |
\( 1 \) |
$1$ |
$26.16385905$ |
0.745412115 |
\( 16581375 \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 7 a - 21\) , \( -6 a + 52\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(7a-21\right){x}-6a+52$ |
| 7.1-a1 |
7.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( -7 \) |
$1.27544$ |
$(a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$39.11307331$ |
1.114337095 |
\( -\frac{152807671423}{7} a + \frac{745053380628}{7} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 116 a - 566\) , \( -1240 a + 6064\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(116a-566\right){x}-1240a+6064$ |
| 7.1-a2 |
7.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{3} \) |
$1.27544$ |
$(a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$39.11307331$ |
1.114337095 |
\( -\frac{37367}{49} a + \frac{175235}{49} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( a - 1\) , \( -2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(a-1\right){x}-2$ |
| 7.1-a3 |
7.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( 7^{6} \) |
$1.27544$ |
$(a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$19.55653665$ |
1.114337095 |
\( \frac{15398559}{343} a + \frac{63253124}{343} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 6 a - 26\) , \( 28 a - 138\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(6a-26\right){x}+28a-138$ |
| 7.1-a4 |
7.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$1.27544$ |
$(a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$19.55653665$ |
1.114337095 |
\( \frac{52244506558836009}{7} a + \frac{203099588968978907}{7} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 111 a - 586\) , \( -1218 a + 6134\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(111a-586\right){x}-1218a+6134$ |
| 7.1-b1 |
7.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{3} \) |
$1.27544$ |
$(a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$6.743487207$ |
$13.81625224$ |
1.769612505 |
\( \frac{37367}{49} a + \frac{137868}{49} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -3 a + 4\) , \( -2 a + 4\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a+4\right){x}-2a+4$ |
| 7.1-b2 |
7.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( 7^{6} \) |
$1.27544$ |
$(a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$3.371743603$ |
$13.81625224$ |
1.769612505 |
\( -\frac{15398559}{343} a + \frac{78651683}{343} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 2 a - 21\) , \( 26 a - 133\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a-21\right){x}+26a-133$ |
| 7.1-b3 |
7.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$1.27544$ |
$(a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$10.11523081$ |
$1.535139138$ |
1.769612505 |
\( -\frac{52244506558836009}{7} a + 36477727932544988 \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 422 a - 2086\) , \( 11275 a - 55139\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(422a-2086\right){x}+11275a-55139$ |
| 7.1-b4 |
7.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( -7 \) |
$1.27544$ |
$(a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$20.23046162$ |
$1.535139138$ |
1.769612505 |
\( \frac{152807671423}{7} a + \frac{592245709205}{7} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 22 a - 131\) , \( 228 a - 1147\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(22a-131\right){x}+228a-1147$ |
| 7.1-c1 |
7.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{3} \) |
$1.27544$ |
$(a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$39.11307331$ |
1.114337095 |
\( \frac{37367}{49} a + \frac{137868}{49} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( -a\) , \( -2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}-a{x}-2$ |
| 7.1-c2 |
7.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( 7^{6} \) |
$1.27544$ |
$(a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$19.55653665$ |
1.114337095 |
\( -\frac{15398559}{343} a + \frac{78651683}{343} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( -6 a - 20\) , \( -28 a - 110\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-6a-20\right){x}-28a-110$ |
| 7.1-c3 |
7.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$1.27544$ |
$(a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$19.55653665$ |
1.114337095 |
\( -\frac{52244506558836009}{7} a + 36477727932544988 \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( -111 a - 475\) , \( 1218 a + 4916\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-111a-475\right){x}+1218a+4916$ |
| 7.1-c4 |
7.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( -7 \) |
$1.27544$ |
$(a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$39.11307331$ |
1.114337095 |
\( \frac{152807671423}{7} a + \frac{592245709205}{7} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( -116 a - 450\) , \( 1240 a + 4824\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-116a-450\right){x}+1240a+4824$ |
| 7.1-d1 |
7.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( -7 \) |
$1.27544$ |
$(a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$20.23046162$ |
$1.535139138$ |
1.769612505 |
\( -\frac{152807671423}{7} a + \frac{745053380628}{7} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -24 a - 109\) , \( -229 a - 919\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-24a-109\right){x}-229a-919$ |
| 7.1-d2 |
7.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{3} \) |
$1.27544$ |
$(a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$6.743487207$ |
$13.81625224$ |
1.769612505 |
\( -\frac{37367}{49} a + \frac{175235}{49} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( a + 1\) , \( a + 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}+a+2$ |
| 7.1-d3 |
7.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( 7^{6} \) |
$1.27544$ |
$(a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$3.371743603$ |
$13.81625224$ |
1.769612505 |
\( \frac{15398559}{343} a + \frac{63253124}{343} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -4 a - 19\) , \( -27 a - 107\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-4a-19\right){x}-27a-107$ |
| 7.1-d4 |
7.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$1.27544$ |
$(a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$10.11523081$ |
$1.535139138$ |
1.769612505 |
\( \frac{52244506558836009}{7} a + \frac{203099588968978907}{7} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -424 a - 1664\) , \( -11276 a - 43864\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-424a-1664\right){x}-11276a-43864$ |
| 11.1-a1 |
11.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$1.42801$ |
$(a-6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 2 \) |
$0.555680735$ |
$8.512583687$ |
2.156261180 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( -70382 a - 273705\) , \( 21156761 a + 82247005\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-70382a-273705\right){x}+21156761a+82247005$ |
| 11.1-a2 |
11.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
11.1 |
\( 11 \) |
\( 11^{10} \) |
$1.42801$ |
$(a-6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \cdot 5 \) |
$0.111136147$ |
$8.512583687$ |
2.156261180 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( -92 a - 355\) , \( 1671 a + 6495\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-92a-355\right){x}+1671a+6495$ |
| 11.1-a3 |
11.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$1.42801$ |
$(a-6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$0.555680735$ |
$8.512583687$ |
2.156261180 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( -2 a - 5\) , \( -19 a - 75\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a-5\right){x}-19a-75$ |
| 11.1-b1 |
11.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$1.42801$ |
$(a-6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 2 \) |
$70.51588395$ |
$0.064435690$ |
2.071228764 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-7820{x}-263580$ |
| 11.1-b2 |
11.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
11.1 |
\( 11 \) |
\( 11^{10} \) |
$1.42801$ |
$(a-6)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.1 |
$1$ |
\( 2 \cdot 5 \) |
$14.10317679$ |
$1.610892258$ |
2.071228764 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-10{x}-20$ |
| 11.1-b3 |
11.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$1.42801$ |
$(a-6)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 2 \) |
$2.820635358$ |
$40.27230645$ |
2.071228764 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}$ |
| 17.1-a1 |
17.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
17.1 |
\( 17 \) |
\( 17^{6} \) |
$1.59219$ |
$(a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Nn |
$4$ |
\( 2 \) |
$1$ |
$1.719733854$ |
1.567854891 |
\( -\frac{16539036917760}{24137569} a - \frac{64295071322112}{24137569} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -2 a - 5\) , \( a - 27\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-2a-5\right){x}+a-27$ |
| 17.1-b1 |
17.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
17.1 |
\( 17 \) |
\( 17^{6} \) |
$1.59219$ |
$(a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Nn |
$1$ |
\( 2 \cdot 3 \) |
$0.127016004$ |
$13.96491997$ |
2.425675946 |
\( -\frac{16539036917760}{24137569} a - \frac{64295071322112}{24137569} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -25 a + 122\) , \( -2451 a + 11979\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-25a+122\right){x}-2451a+11979$ |
| 17.2-a1 |
17.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
17.2 |
\( 17 \) |
\( 17^{6} \) |
$1.59219$ |
$(a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Nn |
$4$ |
\( 2 \) |
$1$ |
$1.719733854$ |
1.567854891 |
\( \frac{16539036917760}{24137569} a - \frac{80834108239872}{24137569} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 2 a - 7\) , \( -a - 26\bigr] \) |
${y}^2+{y}={x}^{3}+\left(2a-7\right){x}-a-26$ |
| 17.2-b1 |
17.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
17.2 |
\( 17 \) |
\( 17^{6} \) |
$1.59219$ |
$(a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Nn |
$1$ |
\( 2 \cdot 3 \) |
$0.127016004$ |
$13.96491997$ |
2.425675946 |
\( \frac{16539036917760}{24137569} a - \frac{80834108239872}{24137569} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 25 a + 97\) , \( 2451 a + 9528\bigr] \) |
${y}^2+{y}={x}^{3}+\left(25a+97\right){x}+2451a+9528$ |
| 23.1-a1 |
23.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
23.1 |
\( 23 \) |
\( 23^{2} \) |
$1.71718$ |
$(a+6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.664676963$ |
$38.88510373$ |
2.945428784 |
\( \frac{41151093}{529} a - \frac{201174001}{529} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -2 a - 2\) , \( 11 a + 39\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-2a-2\right){x}+11a+39$ |
| 23.1-a2 |
23.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
23.1 |
\( 23 \) |
\( 23 \) |
$1.71718$ |
$(a+6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.329353927$ |
$38.88510373$ |
2.945428784 |
\( -\frac{1224298528787}{23} a + \frac{5983743984822}{23} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -57 a - 217\) , \( 393 a + 1526\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-57a-217\right){x}+393a+1526$ |
| 23.1-b1 |
23.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
23.1 |
\( 23 \) |
\( 23^{2} \) |
$1.71718$ |
$(a+6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$5.199911754$ |
$4.540262683$ |
2.690491294 |
\( \frac{41151093}{529} a - \frac{201174001}{529} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -2 a + 11\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a+11\right){x}$ |
| 23.1-b2 |
23.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
23.1 |
\( 23 \) |
\( 23 \) |
$1.71718$ |
$(a+6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$10.39982350$ |
$4.540262683$ |
2.690491294 |
\( -\frac{1224298528787}{23} a + \frac{5983743984822}{23} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 8 a - 44\) , \( 73 a - 367\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(8a-44\right){x}+73a-367$ |
| 23.2-a1 |
23.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
23.2 |
\( 23 \) |
\( 23^{2} \) |
$1.71718$ |
$(a-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.664676963$ |
$38.88510373$ |
2.945428784 |
\( -\frac{41151093}{529} a - \frac{160022908}{529} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( a - 3\) , \( -12 a + 51\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(a-3\right){x}-12a+51$ |
| 23.2-a2 |
23.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
23.2 |
\( 23 \) |
\( 23 \) |
$1.71718$ |
$(a-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.329353927$ |
$38.88510373$ |
2.945428784 |
\( \frac{1224298528787}{23} a + \frac{4759445456035}{23} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 56 a - 273\) , \( -394 a + 1920\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(56a-273\right){x}-394a+1920$ |
| 23.2-b1 |
23.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
23.2 |
\( 23 \) |
\( 23^{2} \) |
$1.71718$ |
$(a-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$5.199911754$ |
$4.540262683$ |
2.690491294 |
\( -\frac{41151093}{529} a - \frac{160022908}{529} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 2 a + 9\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(2a+9\right){x}$ |
| 23.2-b2 |
23.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
23.2 |
\( 23 \) |
\( 23 \) |
$1.71718$ |
$(a-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$10.39982350$ |
$4.540262683$ |
2.690491294 |
\( \frac{1224298528787}{23} a + \frac{4759445456035}{23} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -8 a - 36\) , \( -73 a - 294\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-8a-36\right){x}-73a-294$ |
| 25.1-a1 |
25.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$1.75335$ |
$(5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3Nn |
$1$ |
\( 1 \) |
$1$ |
$12.17791294$ |
1.387801979 |
\( -\frac{110592}{125} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -a - 4\) , \( -2 a - 8\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-4\right){x}-2a-8$ |
| 25.1-b1 |
25.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$1.75335$ |
$(5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3Nn |
$1$ |
\( 1 \) |
$1$ |
$12.17791294$ |
1.387801979 |
\( -\frac{110592}{125} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( a - 5\) , \( 2 a - 10\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a-5\right){x}+2a-10$ |
| 28.1-a1 |
28.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{36} \cdot 7^{2} \) |
$1.80374$ |
$(a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.210429933$ |
$7.027708105$ |
3.033530572 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -1536 a - 5960\) , \( 66830 a + 259805\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-1536a-5960\right){x}+66830a+259805$ |
| 28.1-a2 |
28.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{2} \) |
$1.80374$ |
$(a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1.893869405$ |
$7.027708105$ |
3.033530572 |
\( -\frac{15625}{28} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( 5 a - 15\) , \( 30 a - 139\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(5a-15\right){x}+30a-139$ |
| 28.1-a3 |
28.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{12} \cdot 7^{6} \) |
$1.80374$ |
$(a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.631289801$ |
$7.027708105$ |
3.033530572 |
\( \frac{9938375}{21952} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 39 a + 165\) , \( 540 a + 2107\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(39a+165\right){x}+540a+2107$ |
| 28.1-a4 |
28.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{6} \cdot 7^{12} \) |
$1.80374$ |
$(a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2 \cdot 3 \) |
$1.262579603$ |
$7.027708105$ |
3.033530572 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -321 a - 1235\) , \( 4940 a + 19211\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-321a-1235\right){x}+4940a+19211$ |
| 28.1-a5 |
28.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{2} \cdot 7^{4} \) |
$1.80374$ |
$(a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$3.787738810$ |
$7.027708105$ |
3.033530572 |
\( \frac{128787625}{98} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -96 a - 360\) , \( -1170 a - 4541\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-96a-360\right){x}-1170a-4541$ |
| 28.1-a6 |
28.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{18} \cdot 7^{4} \) |
$1.80374$ |
$(a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.420859867$ |
$7.027708105$ |
3.033530572 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -24576 a - 95560\) , \( 4362510 a + 16959197\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-24576a-95560\right){x}+4362510a+16959197$ |
| 28.1-b1 |
28.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{36} \cdot 7^{2} \) |
$1.80374$ |
$(a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.436190660$ |
1.789507409 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-171{x}-874$ |
| 28.1-b2 |
28.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{2} \) |
$1.80374$ |
$(a+3), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2^{2} \) |
$1$ |
$35.33144352$ |
1.789507409 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}$ |
| 28.1-b3 |
28.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{12} \cdot 7^{6} \) |
$1.80374$ |
$(a+3), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$4$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$3.925715946$ |
1.789507409 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+4{x}-6$ |
| 28.1-b4 |
28.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{6} \cdot 7^{12} \) |
$1.80374$ |
$(a+3), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$4$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$3.925715946$ |
1.789507409 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-36{x}-70$ |
*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.
