| 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 |
| 16.1-a1 |
16.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
16.1 |
\( 2^{4} \) |
\( 2^{42} \) |
$1.28875$ |
$(2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3Ns, 5B |
$1$ |
\( 2 \) |
$1.688026059$ |
$0.987129325$ |
1.848593902 |
\( -\frac{1680914269}{32768} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( a + 101\) , \( -124 a - 99\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3-a{x}^2+\left(a+101\right){x}-124a-99$ |
| 16.1-a2 |
16.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
16.1 |
\( 2^{4} \) |
\( 2^{18} \) |
$1.28875$ |
$(2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3Ns, 5B |
$1$ |
\( 2 \) |
$0.337605211$ |
$4.935646628$ |
1.848593902 |
\( \frac{1331}{8} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( a + 1\) , \( 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3-a{x}^2+\left(a+1\right){x}+1$ |
| 16.1-b1 |
16.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
16.1 |
\( 2^{4} \) |
\( 2^{42} \) |
$1.28875$ |
$(2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3Ns, 5B |
$1$ |
\( 2 \) |
$1.688026059$ |
$0.987129325$ |
1.848593902 |
\( -\frac{1680914269}{32768} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -a + 101\) , \( 124 a - 99\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(-a+101\right){x}+124a-99$ |
| 16.1-b2 |
16.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
16.1 |
\( 2^{4} \) |
\( 2^{18} \) |
$1.28875$ |
$(2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3Ns, 5B |
$1$ |
\( 2 \) |
$0.337605211$ |
$4.935646628$ |
1.848593902 |
\( \frac{1331}{8} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -a + 1\) , \( 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(-a+1\right){x}+1$ |
| 26.1-a1 |
26.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{18} \cdot 13^{2} \) |
$1.45507$ |
$(2,a+1), (a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$0.896934130$ |
0.995059076 |
\( -\frac{10730978619193}{6656} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -460\) , \( -3830\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-460{x}-3830$ |
| 26.1-a2 |
26.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{6} \cdot 13^{6} \) |
$1.45507$ |
$(2,a+1), (a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$2.690802392$ |
0.995059076 |
\( -\frac{10218313}{17576} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -5\) , \( -8\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-5{x}-8$ |
| 26.1-a3 |
26.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{2} \cdot 13^{2} \) |
$1.45507$ |
$(2,a+1), (a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$8.072407178$ |
0.995059076 |
\( \frac{12167}{26} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3$ |
| 26.1-b1 |
26.1-b |
$2$ |
$7$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{2} \cdot 13^{14} \) |
$1.45507$ |
$(2,a+1), (a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.6.1 |
$1$ |
\( 2^{2} \) |
$1.383448027$ |
$0.560128502$ |
1.719367970 |
\( -\frac{1064019559329}{125497034} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -211\) , \( 1469\bigr] \) |
${y}^2+a{x}{y}={x}^3+{x}^2-211{x}+1469$ |
| 26.1-b2 |
26.1-b |
$2$ |
$7$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{14} \cdot 13^{2} \) |
$1.45507$ |
$(2,a+1), (a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.6.1 |
$1$ |
\( 2^{2} \) |
$0.197635432$ |
$3.920899519$ |
1.719367970 |
\( -\frac{2146689}{1664} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -1\) , \( -1\bigr] \) |
${y}^2+a{x}{y}={x}^3+{x}^2-{x}-1$ |
| 26.1-c1 |
26.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{18} \cdot 13^{2} \) |
$1.45507$ |
$(2,a+1), (a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.166288191$ |
$0.896934130$ |
2.978398339 |
\( -\frac{10730978619193}{6656} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -456\) , \( 4288\bigr] \) |
${y}^2+a{x}{y}={x}^3-456{x}+4288$ |
| 26.1-c2 |
26.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{6} \cdot 13^{6} \) |
$1.45507$ |
$(2,a+1), (a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.055429397$ |
$2.690802392$ |
2.978398339 |
\( -\frac{10218313}{17576} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -1\) , \( 11\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}+11$ |
| 26.1-c3 |
26.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{2} \cdot 13^{2} \) |
$1.45507$ |
$(2,a+1), (a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$0.166288191$ |
$8.072407178$ |
2.978398339 |
\( \frac{12167}{26} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 4\) , \( -2\bigr] \) |
${y}^2+a{x}{y}={x}^3+4{x}-2$ |
| 26.1-d1 |
26.1-d |
$2$ |
$7$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{2} \cdot 13^{14} \) |
$1.45507$ |
$(2,a+1), (a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$4$ |
\( 2^{2} \) |
$1$ |
$0.560128502$ |
2.485627123 |
\( -\frac{1064019559329}{125497034} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -213\) , \( -1257\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-213{x}-1257$ |
| 26.1-d2 |
26.1-d |
$2$ |
$7$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{14} \cdot 13^{2} \) |
$1.45507$ |
$(2,a+1), (a)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$4$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$3.920899519$ |
2.485627123 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 49.1-a1 |
49.1-a |
$2$ |
$7$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
49.1 |
\( 7^{2} \) |
\( 7^{6} \) |
$1.70486$ |
$(7,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 7$ |
3Nn, 7B |
$1$ |
\( 1 \) |
$1$ |
$4.561503326$ |
1.265133395 |
\( -3703 a + 11250 \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( -a + 5\) , \( -a - 2\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(-a+5\right){x}-a-2$ |
| 49.1-a2 |
49.1-a |
$2$ |
$7$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
49.1 |
\( 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$1.70486$ |
$(7,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 7$ |
3Nn, 7B |
$1$ |
\( 1 \) |
$1$ |
$4.561503326$ |
1.265133395 |
\( 3703 a + 11250 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -6 a - 13\) , \( a + 43\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(-6a-13\right){x}+a+43$ |
| 49.1-b1 |
49.1-b |
$2$ |
$7$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
49.1 |
\( 7^{2} \) |
\( 7^{6} \) |
$1.70486$ |
$(7,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 7$ |
3Nn, 7B.2.3 |
$1$ |
\( 1 \) |
$1$ |
$4.561503326$ |
1.265133395 |
\( -3703 a + 11250 \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( a - 3\) , \( 11\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3+\left(-a-1\right){x}^2+\left(a-3\right){x}+11$ |
| 49.1-b2 |
49.1-b |
$2$ |
$7$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
49.1 |
\( 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$1.70486$ |
$(7,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 7$ |
3Nn, 7B.2.3 |
$1$ |
\( 1 \) |
$1$ |
$4.561503326$ |
1.265133395 |
\( 3703 a + 11250 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -7 a - 15\) , \( -6 a + 37\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a-1\right){x}^2+\left(-7a-15\right){x}-6a+37$ |
| 49.3-a1 |
49.3-a |
$2$ |
$7$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
49.3 |
\( 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$1.70486$ |
$(7,a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 7$ |
3Nn, 7B |
$1$ |
\( 1 \) |
$1$ |
$4.561503326$ |
1.265133395 |
\( -3703 a + 11250 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( a - 19\) , \( -14 a + 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a+1\right){x}^2+\left(a-19\right){x}-14a+1$ |
| 49.3-a2 |
49.3-a |
$2$ |
$7$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
49.3 |
\( 7^{2} \) |
\( 7^{6} \) |
$1.70486$ |
$(7,a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 7$ |
3Nn, 7B |
$1$ |
\( 1 \) |
$1$ |
$4.561503326$ |
1.265133395 |
\( 3703 a + 11250 \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 5\) , \( -2\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+5{x}-2$ |
| 49.3-b1 |
49.3-b |
$2$ |
$7$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
49.3 |
\( 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$1.70486$ |
$(7,a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 7$ |
3Nn, 7B.2.1 |
$1$ |
\( 1 \) |
$1$ |
$4.561503326$ |
1.265133395 |
\( -3703 a + 11250 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -2 a - 9\) , \( -3 a + 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a-1\right){x}^2+\left(-2a-9\right){x}-3a+1$ |
| 49.3-b2 |
49.3-b |
$2$ |
$7$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
49.3 |
\( 7^{2} \) |
\( 7^{6} \) |
$1.70486$ |
$(7,a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 7$ |
3Nn, 7B.2.1 |
$1$ |
\( 1 \) |
$1$ |
$4.561503326$ |
1.265133395 |
\( 3703 a + 11250 \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -2 a - 3\) , \( 11\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3+\left(a-1\right){x}^2+\left(-2a-3\right){x}+11$ |
| 52.1-a1 |
52.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{16} \cdot 13^{4} \) |
$1.73038$ |
$(2,a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4.738620278$ |
0.657128399 |
\( \frac{432}{169} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( -10\bigr] \) |
${y}^2={x}^3+{x}-10$ |
| 52.1-a2 |
52.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{8} \cdot 13^{2} \) |
$1.73038$ |
$(2,a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4.738620278$ |
0.657128399 |
\( \frac{442368}{13} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4\) , \( -3\bigr] \) |
${y}^2={x}^3-4{x}-3$ |
| 52.1-b1 |
52.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{16} \cdot 13^{4} \) |
$1.73038$ |
$(2,a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$4.738620278$ |
1.971385198 |
\( \frac{432}{169} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 10\bigr] \) |
${y}^2={x}^3+{x}+10$ |
| 52.1-b2 |
52.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{8} \cdot 13^{2} \) |
$1.73038$ |
$(2,a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$4.738620278$ |
1.971385198 |
\( \frac{442368}{13} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4\) , \( 3\bigr] \) |
${y}^2={x}^3-4{x}+3$ |
| 64.1-a1 |
64.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
64.1 |
\( 2^{6} \) |
\( 2^{6} \) |
$1.82257$ |
$(2,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3$ |
3Cn |
$1$ |
\( 1 \) |
$1$ |
$7.681576726$ |
2.130486058 |
\( -74088 \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -4 a + 1\) , \( 10\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+a{x}^2+\left(-4a+1\right){x}+10$ |
| 64.1-b1 |
64.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
64.1 |
\( 2^{6} \) |
\( 2^{12} \) |
$1.82257$ |
$(2,a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$5.832511736$ |
$6.875185818$ |
2.780407135 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^3-{x}$ |
| 64.1-b2 |
64.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
64.1 |
\( 2^{6} \) |
\( 2^{24} \) |
$1.82257$ |
$(2,a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$2.916255868$ |
$6.875185818$ |
2.780407135 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4\) , \( 0\bigr] \) |
${y}^2={x}^3+4{x}$ |
| 64.1-b3 |
64.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
64.1 |
\( 2^{6} \) |
\( 2^{18} \) |
$1.82257$ |
$(2,a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$2.916255868$ |
$6.875185818$ |
2.780407135 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -11\) , \( -14\bigr] \) |
${y}^2={x}^3-11{x}-14$ |
| 64.1-b4 |
64.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
64.1 |
\( 2^{6} \) |
\( 2^{18} \) |
$1.82257$ |
$(2,a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$11.66502347$ |
$6.875185818$ |
2.780407135 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -11\) , \( 14\bigr] \) |
${y}^2={x}^3-11{x}+14$ |
| 64.1-c1 |
64.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
64.1 |
\( 2^{6} \) |
\( 2^{6} \) |
$1.82257$ |
$(2,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3$ |
3Cn |
$1$ |
\( 1 \) |
$1$ |
$7.681576726$ |
2.130486058 |
\( -74088 \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -3 a - 5\) , \( a + 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+a{x}^2+\left(-3a-5\right){x}+a+7$ |
| 72.1-a1 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{16} \) |
$1.87704$ |
$(2,a+1), (3)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$11.45024622$ |
$1.817673508$ |
2.886217342 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 16\) , \( 180\bigr] \) |
${y}^2={x}^3+{x}^2+16{x}+180$ |
| 72.1-a2 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$1.87704$ |
$(2,a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1.431280778$ |
$7.270694035$ |
2.886217342 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^3+{x}^2+{x}$ |
| 72.1-a3 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{4} \) |
$1.87704$ |
$(2,a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$2.862561557$ |
$7.270694035$ |
2.886217342 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -4\) , \( -4\bigr] \) |
${y}^2={x}^3+{x}^2-4{x}-4$ |
| 72.1-a4 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{8} \) |
$1.87704$ |
$(2,a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$5.725123114$ |
$3.635347017$ |
2.886217342 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -24\) , \( 36\bigr] \) |
${y}^2={x}^3+{x}^2-24{x}+36$ |
| 72.1-a5 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{2} \) |
$1.87704$ |
$(2,a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1.431280778$ |
$3.635347017$ |
2.886217342 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -64\) , \( -220\bigr] \) |
${y}^2={x}^3+{x}^2-64{x}-220$ |
| 72.1-a6 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{4} \) |
$1.87704$ |
$(2,a+1), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$11.45024622$ |
$1.817673508$ |
2.886217342 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -384\) , \( 2772\bigr] \) |
${y}^2={x}^3+{x}^2-384{x}+2772$ |
| 72.1-b1 |
72.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{16} \) |
$1.87704$ |
$(2,a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.817673508$ |
2.016527704 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 16\) , \( -180\bigr] \) |
${y}^2={x}^3-{x}^2+16{x}-180$ |
| 72.1-b2 |
72.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$1.87704$ |
$(2,a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$7.270694035$ |
2.016527704 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^3-{x}^2+{x}$ |
| 72.1-b3 |
72.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{4} \) |
$1.87704$ |
$(2,a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$16$ |
\( 2^{2} \) |
$1$ |
$7.270694035$ |
2.016527704 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -4\) , \( 4\bigr] \) |
${y}^2={x}^3-{x}^2-4{x}+4$ |
| 72.1-b4 |
72.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{8} \) |
$1.87704$ |
$(2,a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$3.635347017$ |
2.016527704 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -24\) , \( -36\bigr] \) |
${y}^2={x}^3-{x}^2-24{x}-36$ |
| 72.1-b5 |
72.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{2} \) |
$1.87704$ |
$(2,a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$16$ |
\( 2 \) |
$1$ |
$3.635347017$ |
2.016527704 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -64\) , \( 220\bigr] \) |
${y}^2={x}^3-{x}^2-64{x}+220$ |
| 72.1-b6 |
72.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{4} \) |
$1.87704$ |
$(2,a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$1.817673508$ |
2.016527704 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -384\) , \( -2772\bigr] \) |
${y}^2={x}^3-{x}^2-384{x}-2772$ |
| 98.2-a1 |
98.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{36} \cdot 7^{2} \) |
$2.02743$ |
$(2,a+1), (7,a+1), (7,a+6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \) |
$10.40550172$ |
$0.875417135$ |
2.526424896 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-171{x}-874$ |
| 98.2-a2 |
98.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{2} \) |
$2.02743$ |
$(2,a+1), (7,a+1), (7,a+6)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \) |
$10.40550172$ |
$7.878754216$ |
2.526424896 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}$ |
| 98.2-a3 |
98.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$2.02743$ |
$(2,a+1), (7,a+1), (7,a+6)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$3.468500574$ |
$2.626251405$ |
2.526424896 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+4{x}-6$ |
| 98.2-a4 |
98.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{12} \) |
$2.02743$ |
$(2,a+1), (7,a+1), (7,a+6)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1.734250287$ |
$1.313125702$ |
2.526424896 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-36{x}-70$ |
| 98.2-a5 |
98.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{2} \cdot 7^{4} \) |
$2.02743$ |
$(2,a+1), (7,a+1), (7,a+6)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{3} \) |
$5.202750861$ |
$3.939377108$ |
2.526424896 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-11{x}+12$ |
| 98.2-a6 |
98.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{4} \) |
$2.02743$ |
$(2,a+1), (7,a+1), (7,a+6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{3} \) |
$5.202750861$ |
$0.437708567$ |
2.526424896 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-2731{x}-55146$ |
*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.
