| 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 |
| 121.1-a1 |
121.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$3.78380$ |
$(11)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.2 |
$4$ |
\( 1 \) |
$1$ |
$0.370308724$ |
0.232038542 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \) |
${y}^2+{y}={x}^3-{x}^2-7820{x}-263580$ |
| 121.1-a2 |
121.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
121.1 |
\( 11^{2} \) |
\( 11^{10} \) |
$3.78380$ |
$(11)$ |
$0$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.1 |
$4$ |
\( 5 \) |
$1$ |
$1.851543623$ |
0.232038542 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \) |
${y}^2+{y}={x}^3-{x}^2-10{x}-20$ |
| 121.1-a3 |
121.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$3.78380$ |
$(11)$ |
$0$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$4$ |
\( 1 \) |
$1$ |
$9.257718117$ |
0.232038542 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{y}={x}^3-{x}^2$ |
| 163.1-a1 |
163.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
163.1 |
\( 163 \) |
\( 163^{2} \) |
$4.07642$ |
$(-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cn |
$4$ |
\( 2 \) |
$0.189909232$ |
$5.483364664$ |
2.610053345 |
\( -\frac{884736}{163} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -2\) , \( 1\bigr] \) |
${y}^2+{y}={x}^3-2{x}+1$ |
| 196.1-a1 |
196.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{36} \cdot 7^{2} \) |
$4.26871$ |
$(2), (7)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.875417135$ |
6.228078249 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-171{x}-874$ |
| 196.1-a2 |
196.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{2} \) |
$4.26871$ |
$(2), (7)$ |
$0 \le r \le 1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$$ |
\( 2 \) |
$1$ |
$7.878754216$ |
6.228078249 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}$ |
| 196.1-a3 |
196.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$4.26871$ |
$(2), (7)$ |
$0 \le r \le 1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$2.626251405$ |
6.228078249 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+4{x}-6$ |
| 196.1-a4 |
196.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{12} \) |
$4.26871$ |
$(2), (7)$ |
$0 \le r \le 1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$1.313125702$ |
6.228078249 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-36{x}-70$ |
| 196.1-a5 |
196.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 7^{4} \) |
$4.26871$ |
$(2), (7)$ |
$0 \le r \le 1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$$ |
\( 2 \) |
$1$ |
$3.939377108$ |
6.228078249 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-11{x}+12$ |
| 196.1-a6 |
196.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{4} \) |
$4.26871$ |
$(2), (7)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.437708567$ |
6.228078249 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-2731{x}-55146$ |
| 225.1-a1 |
225.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{32} \cdot 5^{2} \) |
$4.41853$ |
$(3), (5)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$$ |
\( 2^{4} \) |
$1$ |
$0.558925428$ |
4.313443944 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-110{x}-880$ |
| 225.1-a2 |
225.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{2} \cdot 5^{2} \) |
$4.41853$ |
$(3), (5)$ |
$0 \le r \le 1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$$ |
\( 1 \) |
$1$ |
$8.942806850$ |
4.313443944 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2$ |
| 225.1-a3 |
225.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{4} \cdot 5^{16} \) |
$4.41853$ |
$(3), (5)$ |
$0 \le r \le 1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$$ |
\( 2^{4} \) |
$1$ |
$1.117850856$ |
4.313443944 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2+35{x}-28$ |
| 225.1-a4 |
225.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{8} \cdot 5^{8} \) |
$4.41853$ |
$(3), (5)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$$ |
\( 2^{4} \) |
$1$ |
$2.235701712$ |
4.313443944 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-10{x}-10$ |
| 225.1-a5 |
225.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{4} \cdot 5^{4} \) |
$4.41853$ |
$(3), (5)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$$ |
\( 2^{2} \) |
$1$ |
$4.471403425$ |
4.313443944 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-5{x}+2$ |
| 225.1-a6 |
225.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{16} \cdot 5^{4} \) |
$4.41853$ |
$(3), (5)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$$ |
\( 2^{4} \) |
$1$ |
$1.117850856$ |
4.313443944 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-135{x}-660$ |
| 225.1-a7 |
225.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{2} \cdot 5^{2} \) |
$4.41853$ |
$(3), (5)$ |
$0 \le r \le 1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$$ |
\( 1 \) |
$1$ |
$2.235701712$ |
4.313443944 |
\( \frac{56667352321}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-80{x}+242$ |
| 225.1-a8 |
225.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{8} \cdot 5^{2} \) |
$4.41853$ |
$(3), (5)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$$ |
\( 2^{2} \) |
$1$ |
$0.558925428$ |
4.313443944 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-2160{x}-39540$ |
| 244.1-a1 |
244.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
244.1 |
\( 2^{2} \cdot 61 \) |
\( 2^{2} \cdot 61^{2} \) |
$4.50900$ |
$(a+4), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1.247542028$ |
$5.847212706$ |
4.570884663 |
\( -\frac{4757391}{7442} a + \frac{9390068}{3721} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( 5 a + 26\) , \( -9 a - 7\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3-a{x}^2+\left(5a+26\right){x}-9a-7$ |
| 244.2-a1 |
244.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
244.2 |
\( 2^{2} \cdot 61 \) |
\( 2^{2} \cdot 61^{2} \) |
$4.50900$ |
$(a-5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1.247542028$ |
$5.847212706$ |
4.570884663 |
\( \frac{4757391}{7442} a + \frac{14022745}{7442} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -6 a + 31\) , \( 9 a - 16\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3-{x}^2+\left(-6a+31\right){x}+9a-16$ |
| 256.1-a1 |
256.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
256.1 |
\( 2^{8} \) |
\( 2^{30} \) |
$4.56344$ |
$(2)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Cn |
$1$ |
\( 2^{2} \) |
$1$ |
$2.142899731$ |
1.342758886 |
\( \frac{132651}{8} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 17\) , \( -4 a + 2\bigr] \) |
${y}^2={x}^3+17{x}-4a+2$ |
| 256.1-b1 |
256.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
256.1 |
\( 2^{8} \) |
\( 2^{30} \) |
$4.56344$ |
$(2)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Cn |
$1$ |
\( 2^{2} \) |
$1$ |
$2.142899731$ |
1.342758886 |
\( \frac{132651}{8} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 17\) , \( 4 a - 2\bigr] \) |
${y}^2={x}^3+17{x}+4a-2$ |
| 289.1-a1 |
289.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
289.1 |
\( 17^{2} \) |
\( 17^{8} \) |
$4.70389$ |
$(17)$ |
$0$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.123938699$ |
0.083179859 |
\( -\frac{35937}{83521} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( -14\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-{x}-14$ |
| 289.1-a2 |
289.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
289.1 |
\( 17^{2} \) |
\( 17^{2} \) |
$4.70389$ |
$(17)$ |
$0$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$8.495754796$ |
0.083179859 |
\( \frac{35937}{17} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-{x}$ |
| 289.1-a3 |
289.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
289.1 |
\( 17^{2} \) |
\( 17^{4} \) |
$4.70389$ |
$(17)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$4.247877398$ |
0.083179859 |
\( \frac{20346417}{289} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -6\) , \( -4\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-6{x}-4$ |
| 289.1-a4 |
289.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
289.1 |
\( 17^{2} \) |
\( 17^{2} \) |
$4.70389$ |
$(17)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$2.123938699$ |
0.083179859 |
\( \frac{82483294977}{17} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -91\) , \( -310\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-91{x}-310$ |
| 361.1-a1 |
361.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
361.1 |
\( 19^{2} \) |
\( 19^{2} \) |
$4.97289$ |
$(19)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$4$ |
\( 1 \) |
$1$ |
$0.935309008$ |
0.586072443 |
\( -\frac{50357871050752}{19} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -769\) , \( -8470\bigr] \) |
${y}^2+{y}={x}^3+{x}^2-769{x}-8470$ |
| 361.1-a2 |
361.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
361.1 |
\( 19^{2} \) |
\( 19^{6} \) |
$4.97289$ |
$(19)$ |
$0$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$4$ |
\( 3 \) |
$1$ |
$2.805927025$ |
0.586072443 |
\( -\frac{89915392}{6859} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -9\) , \( -15\bigr] \) |
${y}^2+{y}={x}^3+{x}^2-9{x}-15$ |
| 361.1-a3 |
361.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
361.1 |
\( 19^{2} \) |
\( 19^{2} \) |
$4.97289$ |
$(19)$ |
$0$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1 |
$4$ |
\( 1 \) |
$1$ |
$8.417781075$ |
0.586072443 |
\( \frac{32768}{19} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 1\) , \( 0\bigr] \) |
${y}^2+{y}={x}^3+{x}^2+{x}$ |
| 400.1-a1 |
400.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
400.1 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{12} \) |
$5.10208$ |
$(2), (5)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$1.070515942$ |
0.754643519 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -36\) , \( -140\bigr] \) |
${y}^2={x}^3+{x}^2-36{x}-140$ |
| 400.1-a2 |
400.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
400.1 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{4} \) |
$5.10208$ |
$(2), (5)$ |
$0$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$9$ |
\( 2 \cdot 3 \) |
$1$ |
$3.211547828$ |
0.754643519 |
\( \frac{21296}{25} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 4\) , \( 4\bigr] \) |
${y}^2={x}^3+{x}^2+4{x}+4$ |
| 400.1-a3 |
400.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
400.1 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{2} \) |
$5.10208$ |
$(2), (5)$ |
$0$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$9$ |
\( 3 \) |
$1$ |
$6.423095656$ |
0.754643519 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^3+{x}^2-{x}$ |
| 400.1-a4 |
400.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
400.1 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{6} \) |
$5.10208$ |
$(2), (5)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 3^{2} \) |
$1$ |
$2.141031885$ |
0.754643519 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -41\) , \( -116\bigr] \) |
${y}^2={x}^3+{x}^2-41{x}-116$ |
| 441.1-a1 |
441.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{2} \cdot 7^{16} \) |
$5.22808$ |
$(3), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$7.677157865$ |
$0.862076929$ |
4.147082535 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -34\) , \( -217\bigr] \) |
${y}^2+{x}{y}={x}^3-34{x}-217$ |
| 441.1-a2 |
441.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{4} \cdot 7^{2} \) |
$5.22808$ |
$(3), (7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$15.35431573$ |
$6.896615437$ |
4.147082535 |
\( \frac{103823}{63} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}$ |
| 441.1-a3 |
441.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{8} \cdot 7^{4} \) |
$5.22808$ |
$(3), (7)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$30.70863146$ |
$3.448307718$ |
4.147082535 |
\( \frac{7189057}{3969} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -4\) , \( -1\bigr] \) |
${y}^2+{x}{y}={x}^3-4{x}-1$ |
| 441.1-a4 |
441.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{16} \cdot 7^{2} \) |
$5.22808$ |
$(3), (7)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$61.41726292$ |
$1.724153859$ |
4.147082535 |
\( \frac{6570725617}{45927} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -39\) , \( 90\bigr] \) |
${y}^2+{x}{y}={x}^3-39{x}+90$ |
| 441.1-a5 |
441.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{4} \cdot 7^{8} \) |
$5.22808$ |
$(3), (7)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$15.35431573$ |
$1.724153859$ |
4.147082535 |
\( \frac{13027640977}{21609} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -49\) , \( -136\bigr] \) |
${y}^2+{x}{y}={x}^3-49{x}-136$ |
| 441.1-a6 |
441.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{2} \cdot 7^{4} \) |
$5.22808$ |
$(3), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$30.70863146$ |
$0.862076929$ |
4.147082535 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -784\) , \( -8515\bigr] \) |
${y}^2+{x}{y}={x}^3-784{x}-8515$ |
| 576.1-a1 |
576.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{16} \) |
$5.58905$ |
$(2), (3)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$$ |
\( 2^{3} \) |
$1$ |
$0.908836754$ |
6.661758943 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 16\) , \( -180\bigr] \) |
${y}^2={x}^3-{x}^2+16{x}-180$ |
| 576.1-a2 |
576.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$5.58905$ |
$(2), (3)$ |
$0 \le r \le 1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$$ |
\( 2 \) |
$1$ |
$7.270694035$ |
6.661758943 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^3-{x}^2+{x}$ |
| 576.1-a3 |
576.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{4} \) |
$5.58905$ |
$(2), (3)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$$ |
\( 2^{3} \) |
$1$ |
$3.635347017$ |
6.661758943 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -4\) , \( 4\bigr] \) |
${y}^2={x}^3-{x}^2-4{x}+4$ |
| 576.1-a4 |
576.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{8} \) |
$5.58905$ |
$(2), (3)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$$ |
\( 2^{3} \) |
$1$ |
$1.817673508$ |
6.661758943 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -24\) , \( -36\bigr] \) |
${y}^2={x}^3-{x}^2-24{x}-36$ |
| 576.1-a5 |
576.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{2} \) |
$5.58905$ |
$(2), (3)$ |
$0 \le r \le 1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$$ |
\( 2 \) |
$1$ |
$1.817673508$ |
6.661758943 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -64\) , \( 220\bigr] \) |
${y}^2={x}^3-{x}^2-64{x}+220$ |
| 576.1-a6 |
576.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{4} \) |
$5.58905$ |
$(2), (3)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$$ |
\( 2 \) |
$1$ |
$0.908836754$ |
6.661758943 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -384\) , \( -2772\bigr] \) |
${y}^2={x}^3-{x}^2-384{x}-2772$ |
| 593.1-a1 |
593.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
593.1 |
\( 593 \) |
\( 593 \) |
$5.62984$ |
$(a+23)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$9$ |
\( 1 \) |
$1$ |
$8.223475941$ |
2.898505559 |
\( \frac{3503}{593} a - \frac{8168}{593} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 46\) , \( -3 a - 14\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+46{x}-3a-14$ |
| 593.1-a2 |
593.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
593.1 |
\( 593 \) |
\( 593^{2} \) |
$5.62984$ |
$(a+23)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$9$ |
\( 2 \) |
$1$ |
$4.111737970$ |
2.898505559 |
\( -\frac{672292257}{351649} a + \frac{6439664009}{351649} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 51\) , \( -4 a - 29\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+51{x}-4a-29$ |
| 593.2-a1 |
593.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
593.2 |
\( 593 \) |
\( 593 \) |
$5.62984$ |
$(a-24)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$9$ |
\( 1 \) |
$1$ |
$8.223475941$ |
2.898505559 |
\( -\frac{3503}{593} a - \frac{4665}{593} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -2 a + 48\) , \( 2 a - 16\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+\left(-2a+48\right){x}+2a-16$ |
| 593.2-a2 |
593.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
593.2 |
\( 593 \) |
\( 593^{2} \) |
$5.62984$ |
$(a-24)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$9$ |
\( 2 \) |
$1$ |
$4.111737970$ |
2.898505559 |
\( \frac{672292257}{351649} a + \frac{5767371752}{351649} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -2 a + 53\) , \( 3 a - 32\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+\left(-2a+53\right){x}+3a-32$ |
| 604.1-a1 |
604.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
604.1 |
\( 2^{2} \cdot 151 \) |
\( 2^{14} \cdot 151^{2} \) |
$5.65577$ |
$(a+10), (2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$3.668638407$ |
$2.482552716$ |
11.41378186 |
\( -\frac{2066959707}{2918528} a - \frac{868213747}{364816} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( a - 2\) , \( 2 a + 16\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3+{x}^2+\left(a-2\right){x}+2a+16$ |
*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.
