| 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 |
| 1176.1-a1 |
1176.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1176.1 |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 7^{2} \) |
$1.81272$ |
$(a+1), (a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.338640835$ |
$12.44134320$ |
2.432461471 |
\( -\frac{83968}{189} a + \frac{483328}{189} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 8 a - 12\) , \( 12 a - 21\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(8a-12\right){x}+12a-21$ |
| 1176.1-a2 |
1176.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1176.1 |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( - 2^{4} \cdot 3^{3} \cdot 7^{4} \) |
$1.81272$ |
$(a+1), (a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.677281670$ |
$6.220671603$ |
2.432461471 |
\( \frac{68356832}{441} a + \frac{5655536}{21} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -72 a + 125\) , \( 377 a - 653\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-72a+125\right){x}+377a-653$ |
| 1176.1-b1 |
1176.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1176.1 |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( 2^{11} \cdot 3^{11} \cdot 7^{6} \) |
$1.81272$ |
$(a+1), (a), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 11 \) |
$1$ |
$0.733537308$ |
2.329293792 |
\( -\frac{165604169543}{250047} a - \frac{31825071395}{27783} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -103 a - 90\) , \( -553 a - 878\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-103a-90\right){x}-553a-878$ |
| 1176.1-c1 |
1176.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1176.1 |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( - 2^{4} \cdot 3^{3} \cdot 7^{4} \) |
$1.81272$ |
$(a+1), (a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.115298284$ |
$16.26643952$ |
3.248448415 |
\( -\frac{68356832}{441} a + \frac{5655536}{21} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 9 a - 10\) , \( -18 a + 35\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(9a-10\right){x}-18a+35$ |
| 1176.1-c2 |
1176.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1176.1 |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 7^{2} \) |
$1.81272$ |
$(a+1), (a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.057649142$ |
$16.26643952$ |
3.248448415 |
\( \frac{83968}{189} a + \frac{483328}{189} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -8 a - 12\) , \( 12 a + 21\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-8a-12\right){x}+12a+21$ |
| 1176.1-d1 |
1176.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1176.1 |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( 2^{11} \cdot 3^{11} \cdot 7^{6} \) |
$1.81272$ |
$(a+1), (a), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$3.215831324$ |
0.928330540 |
\( -\frac{165604169543}{250047} a - \frac{31825071395}{27783} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -103 a - 87\) , \( 450 a + 789\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-103a-87\right){x}+450a+789$ |
| 1176.1-e1 |
1176.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1176.1 |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 7^{8} \) |
$1.81272$ |
$(a+1), (a), (7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.149717591$ |
$3.694103890$ |
2.452108338 |
\( \frac{11696828}{7203} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -48 a + 83\) , \( 42 a - 73\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-48a+83\right){x}+42a-73$ |
| 1176.1-e2 |
1176.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1176.1 |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 7^{4} \) |
$1.81272$ |
$(a+1), (a), (7)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.574858795$ |
$14.77641556$ |
2.452108338 |
\( \frac{810448}{441} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 12 a - 22\) , \( 12 a - 22\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(12a-22\right){x}+12a-22$ |
| 1176.1-e3 |
1176.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1176.1 |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
$1.81272$ |
$(a+1), (a), (7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.287429397$ |
$29.55283112$ |
2.452108338 |
\( \frac{2725888}{21} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -7\) , \( 10\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-7{x}+10$ |
| 1176.1-e4 |
1176.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1176.1 |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 7^{2} \) |
$1.81272$ |
$(a+1), (a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.149717591$ |
$3.694103890$ |
2.452108338 |
\( \frac{381775972}{567} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 152 a - 267\) , \( 1412 a - 2451\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(152a-267\right){x}+1412a-2451$ |
| 1176.1-f1 |
1176.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1176.1 |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( - 2^{4} \cdot 3^{3} \cdot 7^{4} \) |
$1.81272$ |
$(a+1), (a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.677281670$ |
$6.220671603$ |
2.432461471 |
\( -\frac{68356832}{441} a + \frac{5655536}{21} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 10 a - 9\) , \( 15 a - 21\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(10a-9\right){x}+15a-21$ |
| 1176.1-f2 |
1176.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1176.1 |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 7^{2} \) |
$1.81272$ |
$(a+1), (a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.338640835$ |
$12.44134320$ |
2.432461471 |
\( \frac{83968}{189} a + \frac{483328}{189} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -8 a - 12\) , \( -12 a - 21\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-8a-12\right){x}-12a-21$ |
| 1176.1-g1 |
1176.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1176.1 |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 7^{2} \) |
$1.81272$ |
$(a+1), (a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.057649142$ |
$16.26643952$ |
3.248448415 |
\( -\frac{83968}{189} a + \frac{483328}{189} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 8 a - 12\) , \( -12 a + 21\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(8a-12\right){x}-12a+21$ |
| 1176.1-g2 |
1176.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1176.1 |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( - 2^{4} \cdot 3^{3} \cdot 7^{4} \) |
$1.81272$ |
$(a+1), (a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.115298284$ |
$16.26643952$ |
3.248448415 |
\( \frac{68356832}{441} a + \frac{5655536}{21} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -72 a + 122\) , \( -449 a + 776\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-72a+122\right){x}-449a+776$ |
| 1176.1-h1 |
1176.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1176.1 |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 7^{8} \) |
$1.81272$ |
$(a+1), (a), (7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.688154321$ |
$4.212324935$ |
3.347164639 |
\( \frac{11696828}{7203} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -48 a + 84\) , \( -90 a + 156\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-48a+84\right){x}-90a+156$ |
| 1176.1-h2 |
1176.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1176.1 |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 7^{4} \) |
$1.81272$ |
$(a+1), (a), (7)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.344077160$ |
$16.84929974$ |
3.347164639 |
\( \frac{810448}{441} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 12 a - 21\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(12a-21\right){x}$ |
| 1176.1-h3 |
1176.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1176.1 |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
$1.81272$ |
$(a+1), (a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.688154321$ |
$8.424649871$ |
3.347164639 |
\( \frac{2725888}{21} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -7\) , \( -10\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-7{x}-10$ |
| 1176.1-h4 |
1176.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1176.1 |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 7^{2} \) |
$1.81272$ |
$(a+1), (a), (7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.172038580$ |
$16.84929974$ |
3.347164639 |
\( \frac{381775972}{567} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 152 a - 266\) , \( -1260 a + 2184\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(152a-266\right){x}-1260a+2184$ |
| 1176.1-i1 |
1176.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1176.1 |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 7^{6} \) |
$1.81272$ |
$(a+1), (a), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.844791635$ |
1.642441216 |
\( -\frac{2685153003520}{343} a + \frac{13952471977984}{1029} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 456 a - 800\) , \( 6644 a - 11499\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(456a-800\right){x}+6644a-11499$ |
| 1176.1-i2 |
1176.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1176.1 |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( - 2^{4} \cdot 3 \cdot 7^{12} \) |
$1.81272$ |
$(a+1), (a), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.422395817$ |
1.642441216 |
\( \frac{17575916384}{352947} a - \frac{1305604080}{16807} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 1599 a - 2767\) , \( 45694 a - 79144\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(1599a-2767\right){x}+45694a-79144$ |
| 1176.1-j1 |
1176.1-j |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1176.1 |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( - 2^{4} \cdot 3 \cdot 7^{12} \) |
$1.81272$ |
$(a+1), (a), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.757060740$ |
2.239270553 |
\( -\frac{17575916384}{352947} a - \frac{1305604080}{16807} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 35 a - 88\) , \( -166 a + 329\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(35a-88\right){x}-166a+329$ |
| 1176.1-j2 |
1176.1-j |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1176.1 |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 7^{6} \) |
$1.81272$ |
$(a+1), (a), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.757060740$ |
2.239270553 |
\( \frac{2685153003520}{343} a + \frac{13952471977984}{1029} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -456 a - 800\) , \( 6644 a + 11499\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-456a-800\right){x}+6644a+11499$ |
| 1176.1-k1 |
1176.1-k |
$1$ |
$1$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1176.1 |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( 2^{11} \cdot 3^{11} \cdot 7^{6} \) |
$1.81272$ |
$(a+1), (a), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 11 \) |
$1$ |
$0.733537308$ |
2.329293792 |
\( \frac{165604169543}{250047} a - \frac{31825071395}{27783} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 101 a - 90\) , \( 552 a - 878\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(101a-90\right){x}+552a-878$ |
| 1176.1-l1 |
1176.1-l |
$1$ |
$1$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1176.1 |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( 2^{11} \cdot 3^{11} \cdot 7^{6} \) |
$1.81272$ |
$(a+1), (a), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$3.215831324$ |
0.928330540 |
\( \frac{165604169543}{250047} a - \frac{31825071395}{27783} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 103 a - 87\) , \( -450 a + 789\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(103a-87\right){x}-450a+789$ |
| 1176.1-m1 |
1176.1-m |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1176.1 |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 7^{8} \) |
$1.81272$ |
$(a+1), (a), (7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$1.435756823$ |
2.486803766 |
\( -\frac{2725888}{64827} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -7\) , \( -52\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-7{x}-52$ |
| 1176.1-m2 |
1176.1-m |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1176.1 |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{24} \cdot 7^{2} \) |
$1.81272$ |
$(a+1), (a), (7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$2.871513647$ |
2.486803766 |
\( \frac{6522128932}{3720087} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 391 a - 688\) , \( -428 a + 740\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(391a-688\right){x}-428a+740$ |
| 1176.1-m3 |
1176.1-m |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1176.1 |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 7^{4} \) |
$1.81272$ |
$(a+1), (a), (7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$2.871513647$ |
2.486803766 |
\( \frac{6940769488}{35721} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 251 a - 443\) , \( 3037 a - 5266\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(251a-443\right){x}+3037a-5266$ |
| 1176.1-m4 |
1176.1-m |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1176.1 |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 7^{2} \) |
$1.81272$ |
$(a+1), (a), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.717878411$ |
2.486803766 |
\( \frac{7080974546692}{189} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 4031 a - 7058\) , \( 187312 a - 324676\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(4031a-7058\right){x}+187312a-324676$ |
| 1176.1-n1 |
1176.1-n |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1176.1 |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( - 2^{4} \cdot 3 \cdot 7^{12} \) |
$1.81272$ |
$(a+1), (a), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.422395817$ |
1.642441216 |
\( -\frac{17575916384}{352947} a - \frac{1305604080}{16807} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 33 a - 89\) , \( 200 a - 418\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(33a-89\right){x}+200a-418$ |
| 1176.1-n2 |
1176.1-n |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1176.1 |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 7^{6} \) |
$1.81272$ |
$(a+1), (a), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.844791635$ |
1.642441216 |
\( \frac{2685153003520}{343} a + \frac{13952471977984}{1029} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -456 a - 800\) , \( -6644 a - 11499\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-456a-800\right){x}-6644a-11499$ |
| 1176.1-o1 |
1176.1-o |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1176.1 |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 7^{6} \) |
$1.81272$ |
$(a+1), (a), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.757060740$ |
2.239270553 |
\( -\frac{2685153003520}{343} a + \frac{13952471977984}{1029} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 456 a - 800\) , \( -6644 a + 11499\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(456a-800\right){x}-6644a+11499$ |
| 1176.1-o2 |
1176.1-o |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1176.1 |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( - 2^{4} \cdot 3 \cdot 7^{12} \) |
$1.81272$ |
$(a+1), (a), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.757060740$ |
2.239270553 |
\( \frac{17575916384}{352947} a - \frac{1305604080}{16807} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 1598 a - 2768\) , \( -46864 a + 81170\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(1598a-2768\right){x}-46864a+81170$ |
| 1176.1-p1 |
1176.1-p |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1176.1 |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 7^{8} \) |
$1.81272$ |
$(a+1), (a), (7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$5.389405448$ |
1.555787343 |
\( -\frac{2725888}{64827} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -7\) , \( 52\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-7{x}+52$ |
| 1176.1-p2 |
1176.1-p |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1176.1 |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{24} \cdot 7^{2} \) |
$1.81272$ |
$(a+1), (a), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.694702724$ |
1.555787343 |
\( \frac{6522128932}{3720087} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 393 a - 685\) , \( 820 a - 1427\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(393a-685\right){x}+820a-1427$ |
| 1176.1-p3 |
1176.1-p |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1176.1 |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 7^{4} \) |
$1.81272$ |
$(a+1), (a), (7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$10.77881089$ |
1.555787343 |
\( \frac{6940769488}{35721} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 253 a - 440\) , \( -2785 a + 4824\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(253a-440\right){x}-2785a+4824$ |
| 1176.1-p4 |
1176.1-p |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1176.1 |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 7^{2} \) |
$1.81272$ |
$(a+1), (a), (7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$10.77881089$ |
1.555787343 |
\( \frac{7080974546692}{189} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 4033 a - 7055\) , \( -183280 a + 317619\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(4033a-7055\right){x}-183280a+317619$ |
*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.
