| 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 |
| 56.3-a1 |
56.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{-951}) \) |
$2$ |
$[0, 1]$ |
56.3 |
\( 2^{3} \cdot 7 \) |
\( 2^{10} \cdot 7^{5} \cdot 61^{12} \) |
$7.53834$ |
$(2,a), (2,a+1), (7,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$6.960875662$ |
0.451443717 |
\( -\frac{498679}{67228} a + \frac{4371167}{33614} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 470 a - 210\) , \( -4469 a - 627515\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+\left(-a-1\right){x}^2+\left(470a-210\right){x}-4469a-627515$ |
| 56.3-b1 |
56.3-b |
$1$ |
$1$ |
\(\Q(\sqrt{-951}) \) |
$2$ |
$[0, 1]$ |
56.3 |
\( 2^{3} \cdot 7 \) |
\( 2^{10} \cdot 7^{5} \cdot 29^{12} \) |
$7.53834$ |
$(2,a), (2,a+1), (7,a)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
|
\( 2 \cdot 3 \) |
$1$ |
$6.960875662$ |
14.02073877 |
\( -\frac{498679}{67228} a + \frac{4371167}{33614} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -86 a - 344\) , \( 3340 a - 33756\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(a-1\right){x}^2+\left(-86a-344\right){x}+3340a-33756$ |
| 56.6-a1 |
56.6-a |
$1$ |
$1$ |
\(\Q(\sqrt{-951}) \) |
$2$ |
$[0, 1]$ |
56.6 |
\( 2^{3} \cdot 7 \) |
\( 2^{10} \cdot 7^{5} \cdot 61^{12} \) |
$7.53834$ |
$(2,a), (2,a+1), (7,a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$6.960875662$ |
0.451443717 |
\( \frac{498679}{67228} a + \frac{1177665}{9604} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -469 a + 22\) , \( 3999 a - 631962\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+{x}^2+\left(-469a+22\right){x}+3999a-631962$ |
| 56.6-b1 |
56.6-b |
$1$ |
$1$ |
\(\Q(\sqrt{-951}) \) |
$2$ |
$[0, 1]$ |
56.6 |
\( 2^{3} \cdot 7 \) |
\( 2^{10} \cdot 7^{5} \cdot 29^{12} \) |
$7.53834$ |
$(2,a), (2,a+1), (7,a+6)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
|
\( 2 \cdot 3 \) |
$1$ |
$6.960875662$ |
14.02073877 |
\( \frac{498679}{67228} a + \frac{1177665}{9604} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -32 a - 549\) , \( -3684 a - 36723\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+a{x}^2+\left(-32a-549\right){x}-3684a-36723$ |
| 75.2-a1 |
75.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-951}) \) |
$2$ |
$[0, 1]$ |
75.2 |
\( 3 \cdot 5^{2} \) |
\( 3^{32} \cdot 5^{2} \) |
$8.10950$ |
$(3,a+1), (5,a+1), (5,a+3)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
|
\( 2 \) |
$1$ |
$1.117850856$ |
3.014597673 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-110{x}-880$ |
| 75.2-a2 |
75.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-951}) \) |
$2$ |
$[0, 1]$ |
75.2 |
\( 3 \cdot 5^{2} \) |
\( 3^{2} \cdot 5^{2} \) |
$8.10950$ |
$(3,a+1), (5,a+1), (5,a+3)$ |
$0 \le r \le 1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
|
\( 2 \) |
$1$ |
$17.88561370$ |
3.014597673 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2$ |
| 75.2-a3 |
75.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-951}) \) |
$2$ |
$[0, 1]$ |
75.2 |
\( 3 \cdot 5^{2} \) |
\( 3^{4} \cdot 5^{16} \) |
$8.10950$ |
$(3,a+1), (5,a+1), (5,a+3)$ |
$0 \le r \le 1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
|
\( 2^{7} \) |
$1$ |
$2.235701712$ |
3.014597673 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2+35{x}-28$ |
| 75.2-a4 |
75.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-951}) \) |
$2$ |
$[0, 1]$ |
75.2 |
\( 3 \cdot 5^{2} \) |
\( 3^{8} \cdot 5^{8} \) |
$8.10950$ |
$(3,a+1), (5,a+1), (5,a+3)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
|
\( 2^{5} \) |
$1$ |
$4.471403425$ |
3.014597673 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-10{x}-10$ |
| 75.2-a5 |
75.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-951}) \) |
$2$ |
$[0, 1]$ |
75.2 |
\( 3 \cdot 5^{2} \) |
\( 3^{4} \cdot 5^{4} \) |
$8.10950$ |
$(3,a+1), (5,a+1), (5,a+3)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
|
\( 2^{3} \) |
$1$ |
$8.942806850$ |
3.014597673 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-5{x}+2$ |
| 75.2-a6 |
75.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-951}) \) |
$2$ |
$[0, 1]$ |
75.2 |
\( 3 \cdot 5^{2} \) |
\( 3^{16} \cdot 5^{4} \) |
$8.10950$ |
$(3,a+1), (5,a+1), (5,a+3)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
|
\( 2^{3} \) |
$1$ |
$2.235701712$ |
3.014597673 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-135{x}-660$ |
| 75.2-a7 |
75.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-951}) \) |
$2$ |
$[0, 1]$ |
75.2 |
\( 3 \cdot 5^{2} \) |
\( 3^{2} \cdot 5^{2} \) |
$8.10950$ |
$(3,a+1), (5,a+1), (5,a+3)$ |
$0 \le r \le 1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
|
\( 2 \) |
$1$ |
$4.471403425$ |
3.014597673 |
\( \frac{56667352321}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-80{x}+242$ |
| 75.2-a8 |
75.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-951}) \) |
$2$ |
$[0, 1]$ |
75.2 |
\( 3 \cdot 5^{2} \) |
\( 3^{8} \cdot 5^{2} \) |
$8.10950$ |
$(3,a+1), (5,a+1), (5,a+3)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
|
\( 2 \) |
$1$ |
$1.117850856$ |
3.014597673 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-2160{x}-39540$ |
| 75.2-b1 |
75.2-b |
$8$ |
$16$ |
\(\Q(\sqrt{-951}) \) |
$2$ |
$[0, 1]$ |
75.2 |
\( 3 \cdot 5^{2} \) |
\( 3^{44} \cdot 5^{2} \) |
$8.10950$ |
$(3,a+1), (5,a+1), (5,a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.117850856$ |
0.289990380 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -990\) , \( 22765\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-990{x}+22765$ |
| 75.2-b2 |
75.2-b |
$8$ |
$16$ |
\(\Q(\sqrt{-951}) \) |
$2$ |
$[0, 1]$ |
75.2 |
\( 3 \cdot 5^{2} \) |
\( 3^{14} \cdot 5^{2} \) |
$8.10950$ |
$(3,a+1), (5,a+1), (5,a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$17.88561370$ |
0.289990380 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 0\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-5$ |
| 75.2-b3 |
75.2-b |
$8$ |
$16$ |
\(\Q(\sqrt{-951}) \) |
$2$ |
$[0, 1]$ |
75.2 |
\( 3 \cdot 5^{2} \) |
\( 3^{16} \cdot 5^{16} \) |
$8.10950$ |
$(3,a+1), (5,a+1), (5,a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.235701712$ |
0.289990380 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 315\) , \( 1066\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2+315{x}+1066$ |
| 75.2-b4 |
75.2-b |
$8$ |
$16$ |
\(\Q(\sqrt{-951}) \) |
$2$ |
$[0, 1]$ |
75.2 |
\( 3 \cdot 5^{2} \) |
\( 3^{20} \cdot 5^{8} \) |
$8.10950$ |
$(3,a+1), (5,a+1), (5,a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$4.471403425$ |
0.289990380 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -90\) , \( 175\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-90{x}+175$ |
| 75.2-b5 |
75.2-b |
$8$ |
$16$ |
\(\Q(\sqrt{-951}) \) |
$2$ |
$[0, 1]$ |
75.2 |
\( 3 \cdot 5^{2} \) |
\( 3^{16} \cdot 5^{4} \) |
$8.10950$ |
$(3,a+1), (5,a+1), (5,a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$8.942806850$ |
0.289990380 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -45\) , \( -104\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-45{x}-104$ |
| 75.2-b6 |
75.2-b |
$8$ |
$16$ |
\(\Q(\sqrt{-951}) \) |
$2$ |
$[0, 1]$ |
75.2 |
\( 3 \cdot 5^{2} \) |
\( 3^{28} \cdot 5^{4} \) |
$8.10950$ |
$(3,a+1), (5,a+1), (5,a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$2.235701712$ |
0.289990380 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -1215\) , \( 16600\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-1215{x}+16600$ |
| 75.2-b7 |
75.2-b |
$8$ |
$16$ |
\(\Q(\sqrt{-951}) \) |
$2$ |
$[0, 1]$ |
75.2 |
\( 3 \cdot 5^{2} \) |
\( 3^{14} \cdot 5^{2} \) |
$8.10950$ |
$(3,a+1), (5,a+1), (5,a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$4.471403425$ |
0.289990380 |
\( \frac{56667352321}{15} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -720\) , \( -7259\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-720{x}-7259$ |
| 75.2-b8 |
75.2-b |
$8$ |
$16$ |
\(\Q(\sqrt{-951}) \) |
$2$ |
$[0, 1]$ |
75.2 |
\( 3 \cdot 5^{2} \) |
\( 3^{20} \cdot 5^{2} \) |
$8.10950$ |
$(3,a+1), (5,a+1), (5,a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$1.117850856$ |
0.289990380 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -19440\) , \( 1048135\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-19440{x}+1048135$ |
| 81.1-a1 |
81.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-951}) \) |
$2$ |
$[0, 1]$ |
81.1 |
\( 3^{4} \) |
\( 3^{10} \) |
$8.26704$ |
$(3,a+1)$ |
$0 \le r \le 1$ |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3, 317$ |
3Cs.1.1, 317Nn.1.105.1 |
|
\( 1 \) |
$1$ |
$5.405752176$ |
3.925193384 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -30\) , \( 63\bigr] \) |
${y}^2+{y}={x}^3-30{x}+63$ |
| 81.1-a2 |
81.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-951}) \) |
$2$ |
$[0, 1]$ |
81.1 |
\( 3^{4} \) |
\( 3^{22} \) |
$8.26704$ |
$(3,a+1)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3, 317$ |
3Cs.1.1, 317Nn.1.105.1 |
|
\( 3 \) |
$1$ |
$5.405752176$ |
3.925193384 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 81.1-a3 |
81.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-951}) \) |
$2$ |
$[0, 1]$ |
81.1 |
\( 3^{4} \) |
\( 3^{18} \) |
$8.26704$ |
$(3,a+1)$ |
$0 \le r \le 1$ |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3, 317$ |
3Cs.1.1, 317Nn.1.105.1 |
|
\( 3 \) |
$1$ |
$16.21725652$ |
3.925193384 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -7\bigr] \) |
${y}^2+{y}={x}^3-7$ |
| 81.1-a4 |
81.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-951}) \) |
$2$ |
$[0, 1]$ |
81.1 |
\( 3^{4} \) |
\( 3^{6} \) |
$8.26704$ |
$(3,a+1)$ |
$0 \le r \le 1$ |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3, 317$ |
3Cs.1.1, 317Nn.1.105.1 |
|
\( 1 \) |
$1$ |
$16.21725652$ |
3.925193384 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{y}={x}^3$ |
| 84.2-a1 |
84.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-951}) \) |
$2$ |
$[0, 1]$ |
84.2 |
\( 2^{2} \cdot 3 \cdot 7 \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{12} \cdot 7^{11} \) |
$8.34255$ |
$(2,a), (3,a+1), (7,a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3^{2} \) |
$4.215559041$ |
$1.227945900$ |
6.042917320 |
\( -\frac{74411403460336}{5931980229} a + \frac{274976720382704}{7626831723} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( -208 a - 7332\) , \( -10431 a - 227551\bigr] \) |
${y}^2+a{y}={x}^3+{x}^2+\left(-208a-7332\right){x}-10431a-227551$ |
| 84.2-b1 |
84.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{-951}) \) |
$2$ |
$[0, 1]$ |
84.2 |
\( 2^{2} \cdot 3 \cdot 7 \) |
\( 2^{8} \cdot 3^{6} \cdot 7^{11} \cdot 73^{12} \) |
$8.34255$ |
$(2,a), (3,a+1), (7,a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$9$ |
\( 2 \) |
$1$ |
$1.227945900$ |
0.716739732 |
\( -\frac{74411403460336}{5931980229} a + \frac{274976720382704}{7626831723} \) |
\( \bigl[0\) , \( a\) , \( a\) , \( -106245 a + 597343\) , \( -17021270 a + 848229687\bigr] \) |
${y}^2+a{y}={x}^3+a{x}^2+\left(-106245a+597343\right){x}-17021270a+848229687$ |
| 84.5-a1 |
84.5-a |
$1$ |
$1$ |
\(\Q(\sqrt{-951}) \) |
$2$ |
$[0, 1]$ |
84.5 |
\( 2^{2} \cdot 3 \cdot 7 \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{12} \cdot 7^{11} \) |
$8.34255$ |
$(2,a+1), (3,a+1), (7,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3^{2} \) |
$4.215559041$ |
$1.227945900$ |
6.042917320 |
\( \frac{74411403460336}{5931980229} a + \frac{1255134411535904}{53387822061} \) |
\( \bigl[0\) , \( 1\) , \( a + 1\) , \( 208 a - 7540\) , \( 10430 a - 237982\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^3+{x}^2+\left(208a-7540\right){x}+10430a-237982$ |
| 84.5-b1 |
84.5-b |
$1$ |
$1$ |
\(\Q(\sqrt{-951}) \) |
$2$ |
$[0, 1]$ |
84.5 |
\( 2^{2} \cdot 3 \cdot 7 \) |
\( 2^{8} \cdot 3^{6} \cdot 7^{11} \cdot 73^{12} \) |
$8.34255$ |
$(2,a+1), (3,a+1), (7,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$9$ |
\( 2 \) |
$1$ |
$1.227945900$ |
0.716739732 |
\( \frac{74411403460336}{5931980229} a + \frac{1255134411535904}{53387822061} \) |
\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( 106245 a + 491098\) , \( 17021269 a + 831208417\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+\left(106245a+491098\right){x}+17021269a+831208417$ |
| 85.2-a1 |
85.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-951}) \) |
$2$ |
$[0, 1]$ |
85.2 |
\( 5 \cdot 17 \) |
\( 5^{5} \cdot 17 \cdot 61^{12} \) |
$8.36727$ |
$(5,a+1), (17,a+16)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$11.13211631$ |
0.360983604 |
\( -\frac{1931079}{53125} a - \frac{70786}{3125} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( 69 a - 2631\) , \( 8020 a - 22706\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3+{x}^2+\left(69a-2631\right){x}+8020a-22706$ |
| 85.2-b1 |
85.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{-951}) \) |
$2$ |
$[0, 1]$ |
85.2 |
\( 5 \cdot 17 \) |
\( 5^{5} \cdot 17 \cdot 29^{12} \) |
$8.36727$ |
$(5,a+1), (17,a+16)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \) |
$1$ |
$11.13211631$ |
1.804918021 |
\( -\frac{1931079}{53125} a - \frac{70786}{3125} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -27 a + 1081\) , \( 2078 a - 9031\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3+\left(-a-1\right){x}^2+\left(-27a+1081\right){x}+2078a-9031$ |
| 85.3-a1 |
85.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{-951}) \) |
$2$ |
$[0, 1]$ |
85.3 |
\( 5 \cdot 17 \) |
\( 5^{5} \cdot 17 \cdot 61^{12} \) |
$8.36727$ |
$(5,a+3), (17,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$11.13211631$ |
0.360983604 |
\( \frac{1931079}{53125} a - \frac{3134441}{53125} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( -70 a - 2562\) , \( -8020 a - 14686\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(-a+1\right){x}^2+\left(-70a-2562\right){x}-8020a-14686$ |
| 85.3-b1 |
85.3-b |
$1$ |
$1$ |
\(\Q(\sqrt{-951}) \) |
$2$ |
$[0, 1]$ |
85.3 |
\( 5 \cdot 17 \) |
\( 5^{5} \cdot 17 \cdot 29^{12} \) |
$8.36727$ |
$(5,a+3), (17,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \) |
$1$ |
$11.13211631$ |
1.804918021 |
\( \frac{1931079}{53125} a - \frac{3134441}{53125} \) |
\( \bigl[a + 1\) , \( 1\) , \( a\) , \( 27 a + 1054\) , \( -2051 a - 5899\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^3+{x}^2+\left(27a+1054\right){x}-2051a-5899$ |
*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.
