| 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 |
| 28.1-a1 |
28.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{36} \cdot 5^{12} \cdot 7^{2} \) |
$1.96087$ |
$(7,a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.875417135$ |
1.651835715 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 512 a + 3249\) , \( -15004 a + 87006\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3-a{x}^2+\left(512a+3249\right){x}-15004a+87006$ |
| 28.1-a2 |
28.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 5^{12} \cdot 7^{2} \) |
$1.96087$ |
$(7,a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$7.878754216$ |
1.651835715 |
\( -\frac{15625}{28} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 2 a + 19\) , \( -52\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3-a{x}^2+\left(2a+19\right){x}-52$ |
| 28.1-a3 |
28.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{12} \cdot 5^{12} \cdot 7^{6} \) |
$1.96087$ |
$(7,a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$2.626251405$ |
1.651835715 |
\( \frac{9938375}{21952} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -13 a - 76\) , \( -66 a + 780\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3-a{x}^2+\left(-13a-76\right){x}-66a+780$ |
| 28.1-a4 |
28.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{6} \cdot 5^{12} \cdot 7^{12} \) |
$1.96087$ |
$(7,a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$1.313125702$ |
1.651835715 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 107 a + 684\) , \( -1330 a + 6108\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3-a{x}^2+\left(107a+684\right){x}-1330a+6108$ |
| 28.1-a5 |
28.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{2} \cdot 5^{12} \cdot 7^{4} \) |
$1.96087$ |
$(7,a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$4$ |
\( 2 \) |
$1$ |
$3.939377108$ |
1.651835715 |
\( \frac{128787625}{98} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 32 a + 209\) , \( 132 a - 1716\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3-a{x}^2+\left(32a+209\right){x}+132a-1716$ |
| 28.1-a6 |
28.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{18} \cdot 5^{12} \cdot 7^{4} \) |
$1.96087$ |
$(7,a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$4$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.437708567$ |
1.651835715 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 8192 a + 51889\) , \( -898716 a + 5796830\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3-a{x}^2+\left(8192a+51889\right){x}-898716a+5796830$ |
| 28.1-b1 |
28.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{36} \cdot 7^{2} \) |
$1.96087$ |
$(7,a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1.025454816$ |
$0.875417135$ |
3.387765781 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-171{x}-874$ |
| 28.1-b2 |
28.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{2} \) |
$1.96087$ |
$(7,a+3), (2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \) |
$9.229093350$ |
$7.878754216$ |
3.387765781 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}$ |
| 28.1-b3 |
28.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{12} \cdot 7^{6} \) |
$1.96087$ |
$(7,a+3), (2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$3.076364450$ |
$2.626251405$ |
3.387765781 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+4{x}-6$ |
| 28.1-b4 |
28.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{6} \cdot 7^{12} \) |
$1.96087$ |
$(7,a+3), (2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$6.152728900$ |
$1.313125702$ |
3.387765781 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-36{x}-70$ |
| 28.1-b5 |
28.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{2} \cdot 7^{4} \) |
$1.96087$ |
$(7,a+3), (2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \) |
$18.45818670$ |
$3.939377108$ |
3.387765781 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-11{x}+12$ |
| 28.1-b6 |
28.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{18} \cdot 7^{4} \) |
$1.96087$ |
$(7,a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$2.050909633$ |
$0.437708567$ |
3.387765781 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-2731{x}-55146$ |
| 43.1-a1 |
43.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
43.1 |
\( 43 \) |
\( 43 \) |
$2.18286$ |
$(a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$9.860661183$ |
2.067356319 |
\( \frac{10279}{43} a + \frac{84829}{43} \) |
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( -4 a - 4\) , \( a + 13\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3+\left(a+1\right){x}^2+\left(-4a-4\right){x}+a+13$ |
| 43.1-b1 |
43.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
43.1 |
\( 43 \) |
\( 5^{12} \cdot 43 \) |
$2.18286$ |
$(a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$9.860661183$ |
2.067356319 |
\( \frac{10279}{43} a + \frac{84829}{43} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -2 a + 15\) , \( -7 a + 5\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(-2a+15\right){x}-7a+5$ |
| 43.2-a1 |
43.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
43.2 |
\( 43 \) |
\( 43 \) |
$2.18286$ |
$(a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$9.860661183$ |
2.067356319 |
\( -\frac{10279}{43} a + \frac{95108}{43} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -8 a + 2\) , \( a + 40\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a-1\right){x}^2+\left(-8a+2\right){x}+a+40$ |
| 43.2-b1 |
43.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
43.2 |
\( 43 \) |
\( 5^{12} \cdot 43 \) |
$2.18286$ |
$(a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$9.860661183$ |
2.067356319 |
\( -\frac{10279}{43} a + \frac{95108}{43} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -13\) , \( a - 18\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-13{x}+a-18$ |
| 49.1-a1 |
49.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
49.1 |
\( 7^{2} \) |
\( 7^{6} \) |
$2.25532$ |
$(7,a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$7, 13$ |
7B.1.5, 13Nn.2.6.1 |
$1$ |
\( 2 \) |
$1$ |
$4.944504600$ |
0.518324919 |
\( -3375 \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -2\) , \( -1\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-2{x}-1$ |
| 49.1-a2 |
49.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
49.1 |
\( 7^{2} \) |
\( 5^{12} \cdot 7^{6} \) |
$2.25532$ |
$(7,a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$7, 13$ |
7B.1.5, 13Nn.2.6.1 |
$1$ |
\( 2 \) |
$1$ |
$4.944504600$ |
0.518324919 |
\( -3375 \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 3 a + 55\) , \( -22 a + 72\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+{x}^2+\left(3a+55\right){x}-22a+72$ |
| 49.1-a3 |
49.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
49.1 |
\( 7^{2} \) |
\( 5^{12} \cdot 7^{6} \) |
$2.25532$ |
$(7,a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$7, 13$ |
7B.1.5, 13Nn.2.6.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$2.472252300$ |
0.518324919 |
\( 16581375 \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 108 a + 720\) , \( -1359 a + 7646\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+{x}^2+\left(108a+720\right){x}-1359a+7646$ |
| 49.1-a4 |
49.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
49.1 |
\( 7^{2} \) |
\( 7^{6} \) |
$2.25532$ |
$(7,a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$7, 13$ |
7B.1.5, 13Nn.2.6.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$2.472252300$ |
0.518324919 |
\( 16581375 \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -37\) , \( -78\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-37{x}-78$ |
| 52.1-a1 |
52.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{18} \cdot 13^{2} \) |
$2.28908$ |
$(13,a+6), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.311629297$ |
$0.896934130$ |
2.109651075 |
\( -\frac{10730978619193}{6656} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -460\) , \( -3830\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-460{x}-3830$ |
| 52.1-a2 |
52.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{6} \cdot 13^{6} \) |
$2.28908$ |
$(13,a+6), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.934887892$ |
$2.690802392$ |
2.109651075 |
\( -\frac{10218313}{17576} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -5\) , \( -8\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-5{x}-8$ |
| 52.1-a3 |
52.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{2} \cdot 13^{2} \) |
$2.28908$ |
$(13,a+6), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \) |
$2.804663676$ |
$8.072407178$ |
2.109651075 |
\( \frac{12167}{26} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3$ |
| 52.1-b1 |
52.1-b |
$2$ |
$7$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{2} \cdot 13^{14} \) |
$2.28908$ |
$(13,a+6), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$9$ |
\( 2 \) |
$1$ |
$0.560128502$ |
2.113827178 |
\( -\frac{1064019559329}{125497034} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -213\) , \( -1257\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-213{x}-1257$ |
| 52.1-b2 |
52.1-b |
$2$ |
$7$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{14} \cdot 13^{2} \) |
$2.28908$ |
$(13,a+6), (2)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$9$ |
\( 2 \cdot 7 \) |
$1$ |
$3.920899519$ |
2.113827178 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 52.1-c1 |
52.1-c |
$2$ |
$7$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{2} \cdot 5^{12} \cdot 13^{14} \) |
$2.28908$ |
$(13,a+6), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.6 |
$1$ |
\( 2 \cdot 7 \) |
$1.383448027$ |
$0.560128502$ |
4.549020063 |
\( -\frac{1064019559329}{125497034} \) |
\( \bigl[a + 1\) , \( 1\) , \( a\) , \( 635 a + 4055\) , \( -20745 a + 130438\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^3+{x}^2+\left(635a+4055\right){x}-20745a+130438$ |
| 52.1-c2 |
52.1-c |
$2$ |
$7$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{14} \cdot 5^{12} \cdot 13^{2} \) |
$2.28908$ |
$(13,a+6), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.6 |
$1$ |
\( 2 \cdot 7 \) |
$0.197635432$ |
$3.920899519$ |
4.549020063 |
\( -\frac{2146689}{1664} \) |
\( \bigl[a + 1\) , \( 1\) , \( a\) , \( 5 a + 65\) , \( 45 a - 392\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^3+{x}^2+\left(5a+65\right){x}+45a-392$ |
| 52.1-d1 |
52.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{18} \cdot 5^{12} \cdot 13^{2} \) |
$2.28908$ |
$(13,a+6), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.896934130$ |
3.384872816 |
\( -\frac{10730978619193}{6656} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 1379 a + 8740\) , \( -64034 a + 392316\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3-a{x}^2+\left(1379a+8740\right){x}-64034a+392316$ |
| 52.1-d2 |
52.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{6} \cdot 5^{12} \cdot 13^{6} \) |
$2.28908$ |
$(13,a+6), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$2.690802392$ |
3.384872816 |
\( -\frac{10218313}{17576} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 14 a + 95\) , \( -152 a + 652\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3-a{x}^2+\left(14a+95\right){x}-152a+652$ |
| 52.1-d3 |
52.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{2} \cdot 5^{12} \cdot 13^{2} \) |
$2.28908$ |
$(13,a+6), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2 \) |
$1$ |
$8.072407178$ |
3.384872816 |
\( \frac{12167}{26} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -a\) , \( 6 a - 14\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3-a{x}^2-a{x}+6a-14$ |
| 63.1-a1 |
63.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{2} \cdot 7^{16} \) |
$2.40157$ |
$(7,a+3), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$0.862076929$ |
0.361480869 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -34\) , \( -217\bigr] \) |
${y}^2+{x}{y}={x}^3-34{x}-217$ |
| 63.1-a2 |
63.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{4} \cdot 7^{2} \) |
$2.40157$ |
$(7,a+3), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$6.896615437$ |
0.361480869 |
\( \frac{103823}{63} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}$ |
| 63.1-a3 |
63.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{8} \cdot 7^{4} \) |
$2.40157$ |
$(7,a+3), (3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$3.448307718$ |
0.361480869 |
\( \frac{7189057}{3969} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -4\) , \( -1\bigr] \) |
${y}^2+{x}{y}={x}^3-4{x}-1$ |
| 63.1-a4 |
63.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{16} \cdot 7^{2} \) |
$2.40157$ |
$(7,a+3), (3)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$1.724153859$ |
0.361480869 |
\( \frac{6570725617}{45927} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -39\) , \( 90\bigr] \) |
${y}^2+{x}{y}={x}^3-39{x}+90$ |
| 63.1-a5 |
63.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{4} \cdot 7^{8} \) |
$2.40157$ |
$(7,a+3), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$1.724153859$ |
0.361480869 |
\( \frac{13027640977}{21609} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -49\) , \( -136\bigr] \) |
${y}^2+{x}{y}={x}^3-49{x}-136$ |
| 63.1-a6 |
63.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{2} \cdot 7^{4} \) |
$2.40157$ |
$(7,a+3), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$0.862076929$ |
0.361480869 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -784\) , \( -8515\bigr] \) |
${y}^2+{x}{y}={x}^3-784{x}-8515$ |
| 63.1-b1 |
63.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{2} \cdot 5^{12} \cdot 7^{16} \) |
$2.40157$ |
$(7,a+3), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$2.671455529$ |
$0.862076929$ |
3.862720269 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 103 a + 656\) , \( -3677 a + 21921\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3-a{x}^2+\left(103a+656\right){x}-3677a+21921$ |
| 63.1-b2 |
63.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{4} \cdot 5^{12} \cdot 7^{2} \) |
$2.40157$ |
$(7,a+3), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$5.342911058$ |
$6.896615437$ |
3.862720269 |
\( \frac{103823}{63} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -2 a - 9\) , \( 5 a + 32\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3-a{x}^2+\left(-2a-9\right){x}+5a+32$ |
| 63.1-b3 |
63.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{8} \cdot 5^{12} \cdot 7^{4} \) |
$2.40157$ |
$(7,a+3), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$2.671455529$ |
$3.448307718$ |
3.862720269 |
\( \frac{7189057}{3969} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 13 a + 86\) , \( -41 a - 51\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3-a{x}^2+\left(13a+86\right){x}-41a-51$ |
| 63.1-b4 |
63.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{16} \cdot 5^{12} \cdot 7^{2} \) |
$2.40157$ |
$(7,a+3), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.335727764$ |
$1.724153859$ |
3.862720269 |
\( \frac{6570725617}{45927} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 118 a + 751\) , \( 1205 a - 11118\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3-a{x}^2+\left(118a+751\right){x}+1205a-11118$ |
| 63.1-b5 |
63.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{4} \cdot 5^{12} \cdot 7^{8} \) |
$2.40157$ |
$(7,a+3), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$5.342911058$ |
$1.724153859$ |
3.862720269 |
\( \frac{13027640977}{21609} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 148 a + 941\) , \( -2471 a + 12684\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3-a{x}^2+\left(148a+941\right){x}-2471a+12684$ |
| 63.1-b6 |
63.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{2} \cdot 5^{12} \cdot 7^{4} \) |
$2.40157$ |
$(7,a+3), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$10.68582211$ |
$0.862076929$ |
3.862720269 |
\( \frac{53297461115137}{147} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 2353 a + 14906\) , \( -140945 a + 881307\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3-a{x}^2+\left(2353a+14906\right){x}-140945a+881307$ |
| 91.1-a1 |
91.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
91.1 |
\( 7 \cdot 13 \) |
\( 7^{2} \cdot 13^{2} \) |
$2.63281$ |
$(7,a+3), (13,a+6)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cn, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1.059245086$ |
$4.379860585$ |
0.864596597 |
\( -\frac{43614208}{91} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -7\) , \( 5\bigr] \) |
${y}^2+{y}={x}^3+{x}^2-7{x}+5$ |
| 91.1-a2 |
91.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
91.1 |
\( 7 \cdot 13 \) |
\( 7^{18} \cdot 13^{2} \) |
$2.63281$ |
$(7,a+3), (13,a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cn, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.117693898$ |
$0.486651176$ |
0.864596597 |
\( -\frac{178643795968}{524596891} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -117\) , \( -1245\bigr] \) |
${y}^2+{y}={x}^3+{x}^2-117{x}-1245$ |
| 91.1-a3 |
91.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
91.1 |
\( 7 \cdot 13 \) |
\( 7^{6} \cdot 13^{6} \) |
$2.63281$ |
$(7,a+3), (13,a+6)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cn, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.353081695$ |
$1.459953528$ |
0.864596597 |
\( \frac{224755712}{753571} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 13\) , \( 42\bigr] \) |
${y}^2+{y}={x}^3+{x}^2+13{x}+42$ |
| 91.1-b1 |
91.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
91.1 |
\( 7 \cdot 13 \) |
\( 5^{12} \cdot 7^{2} \cdot 13^{2} \) |
$2.63281$ |
$(7,a+3), (13,a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cn, 3B |
$1$ |
\( 2^{2} \) |
$0.556657989$ |
$4.379860585$ |
4.089291033 |
\( -\frac{43614208}{91} \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 23 a + 132\) , \( 62 a - 694\bigr] \) |
${y}^2+{y}={x}^3+\left(-a-1\right){x}^2+\left(23a+132\right){x}+62a-694$ |
| 91.1-b2 |
91.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
91.1 |
\( 7 \cdot 13 \) |
\( 5^{12} \cdot 7^{18} \cdot 13^{2} \) |
$2.63281$ |
$(7,a+3), (13,a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cn, 3B |
$1$ |
\( 2^{2} \) |
$5.009921908$ |
$0.486651176$ |
4.089291033 |
\( -\frac{178643795968}{524596891} \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 353 a + 2222\) , \( -20268 a + 130966\bigr] \) |
${y}^2+{y}={x}^3+\left(-a-1\right){x}^2+\left(353a+2222\right){x}-20268a+130966$ |
| 91.1-b3 |
91.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
91.1 |
\( 7 \cdot 13 \) |
\( 5^{12} \cdot 7^{6} \cdot 13^{6} \) |
$2.63281$ |
$(7,a+3), (13,a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cn, 3B |
$1$ |
\( 2^{2} \) |
$1.669973969$ |
$1.459953528$ |
4.089291033 |
\( \frac{224755712}{753571} \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -37 a - 248\) , \( 714 a - 4273\bigr] \) |
${y}^2+{y}={x}^3+\left(-a-1\right){x}^2+\left(-37a-248\right){x}+714a-4273$ |
| 91.1-c1 |
91.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
91.1 |
\( 7 \cdot 13 \) |
\( 7^{2} \cdot 13^{2} \) |
$2.63281$ |
$(7,a+3), (13,a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cn |
$1$ |
\( 2^{2} \) |
$0.142392150$ |
$6.505570680$ |
1.553712771 |
\( \frac{110592}{91} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 1\) , \( 0\bigr] \) |
${y}^2+{y}={x}^3+{x}$ |
| 91.1-d1 |
91.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
91.1 |
\( 7 \cdot 13 \) |
\( 5^{12} \cdot 7^{2} \cdot 13^{2} \) |
$2.63281$ |
$(7,a+3), (13,a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cn |
$1$ |
\( 2^{2} \) |
$0.513244526$ |
$6.505570680$ |
5.600270610 |
\( \frac{110592}{91} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -3 a - 19\) , \( 4 a - 27\bigr] \) |
${y}^2+{y}={x}^3+\left(-3a-19\right){x}+4a-27$ |
*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.
