| 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 |
| 20.1-a1 |
20.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{12} \cdot 13^{12} \) |
$4.30921$ |
$(2,a), (5,a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \cdot 3 \) |
$2.011236000$ |
$4.282063771$ |
9.064121843 |
\( -\frac{20720464}{15625} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -1161\) , \( 50881\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2-1161{x}+50881$ |
| 20.1-a2 |
20.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{4} \cdot 13^{12} \) |
$4.30921$ |
$(2,a), (5,a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$2.011236000$ |
$12.84619131$ |
9.064121843 |
\( \frac{21296}{25} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 529\) , \( -3875\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2+529{x}-3875$ |
| 20.1-a3 |
20.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{14} \) |
$4.30921$ |
$(2,a), (5,a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$8.044944002$ |
$12.84619131$ |
9.064121843 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -33\) , \( 62\bigr] \) |
${y}^2={x}^3-{x}^2-33{x}+62$ |
| 20.1-a4 |
20.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{18} \) |
$4.30921$ |
$(2,a), (5,a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$8.044944002$ |
$4.282063771$ |
9.064121843 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -1033\) , \( -12438\bigr] \) |
${y}^2={x}^3-{x}^2-1033{x}-12438$ |
| 20.1-b1 |
20.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{16} \cdot 5^{12} \) |
$4.30921$ |
$(2,a), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$16$ |
\( 2 \) |
$1$ |
$4.282063771$ |
1.502247347 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -36\) , \( -140\bigr] \) |
${y}^2={x}^3+{x}^2-36{x}-140$ |
| 20.1-b2 |
20.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{16} \cdot 5^{4} \) |
$4.30921$ |
$(2,a), (5,a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$16$ |
\( 2 \cdot 3 \) |
$1$ |
$12.84619131$ |
1.502247347 |
\( \frac{21296}{25} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 4\) , \( 4\bigr] \) |
${y}^2={x}^3+{x}^2+4{x}+4$ |
| 20.1-b3 |
20.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$4.30921$ |
$(2,a), (5,a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$16$ |
\( 2 \cdot 3 \) |
$1$ |
$12.84619131$ |
1.502247347 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^3+{x}^2-{x}$ |
| 20.1-b4 |
20.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{6} \) |
$4.30921$ |
$(2,a), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$16$ |
\( 2 \) |
$1$ |
$4.282063771$ |
1.502247347 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -41\) , \( -116\bigr] \) |
${y}^2={x}^3+{x}^2-41{x}-116$ |
| 20.1-c1 |
20.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{12} \) |
$4.30921$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$36$ |
\( 2^{2} \cdot 3 \) |
$0.137812304$ |
$4.282063771$ |
5.589760568 |
\( -\frac{20720464}{15625} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 365\) , \( -1275\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2+365{x}-1275$ |
| 20.1-c2 |
20.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{4} \) |
$4.30921$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \cdot 3 \) |
$0.413436914$ |
$12.84619131$ |
5.589760568 |
\( \frac{21296}{25} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 375\) , \( -1403\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2+375{x}-1403$ |
| 20.1-c3 |
20.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{20} \cdot 5^{2} \) |
$4.30921$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \cdot 3 \) |
$0.826873828$ |
$12.84619131$ |
5.589760568 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -5\) , \( -5\bigr] \) |
${y}^2={x}^3+{x}^2-5{x}-5$ |
| 20.1-c4 |
20.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{20} \cdot 5^{6} \) |
$4.30921$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$36$ |
\( 2 \cdot 3 \) |
$0.275624609$ |
$4.282063771$ |
5.589760568 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -165\) , \( 763\bigr] \) |
${y}^2={x}^3+{x}^2-165{x}+763$ |
| 20.1-d1 |
20.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{24} \) |
$4.30921$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \cdot 3^{2} \) |
$0.516674109$ |
$4.282063771$ |
6.985550797 |
\( -\frac{20720464}{15625} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 190\) , \( 3220\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+190{x}+3220$ |
| 20.1-d2 |
20.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{16} \) |
$4.30921$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \) |
$1.550022328$ |
$12.84619131$ |
6.985550797 |
\( \frac{21296}{25} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 440\) , \( -1530\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+440{x}-1530$ |
| 20.1-d3 |
20.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \cdot 13^{12} \) |
$4.30921$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$3.100044657$ |
$12.84619131$ |
6.985550797 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -225\) , \( 820\bigr] \) |
${y}^2={x}^3+{x}^2-225{x}+820$ |
| 20.1-d4 |
20.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{6} \cdot 13^{12} \) |
$4.30921$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \cdot 3^{2} \) |
$1.033348219$ |
$4.282063771$ |
6.985550797 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -6985\) , \( -226992\bigr] \) |
${y}^2={x}^3+{x}^2-6985{x}-226992$ |
| 26.1-a1 |
26.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{18} \cdot 13^{2} \) |
$4.60133$ |
$(2,a), (13,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$1.793868261$ |
0.314665308 |
\( -\frac{10730978619193}{6656} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -460\) , \( -3830\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-460{x}-3830$ |
| 26.1-a2 |
26.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{6} \cdot 13^{6} \) |
$4.60133$ |
$(2,a), (13,a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$5.381604785$ |
0.314665308 |
\( -\frac{10218313}{17576} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -5\) , \( -8\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-5{x}-8$ |
| 26.1-a3 |
26.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{2} \cdot 13^{2} \) |
$4.60133$ |
$(2,a), (13,a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$16.14481435$ |
0.314665308 |
\( \frac{12167}{26} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3$ |
| 26.1-b1 |
26.1-b |
$2$ |
$7$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{2} \cdot 5^{12} \cdot 13^{14} \) |
$4.60133$ |
$(2,a), (13,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.6.1 |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$1.120257005$ |
1.375542546 |
\( -\frac{1064019559329}{125497034} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -5317\) , \( -162409\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-5317{x}-162409$ |
| 26.1-b2 |
26.1-b |
$2$ |
$7$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{14} \cdot 5^{12} \cdot 13^{2} \) |
$4.60133$ |
$(2,a), (13,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.6.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$7.841799039$ |
1.375542546 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -67\) , \( 341\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-67{x}+341$ |
| 26.1-c1 |
26.1-c |
$2$ |
$7$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{2} \cdot 13^{26} \) |
$4.60133$ |
$(2,a), (13,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.6.1 |
$9$ |
\( 2^{2} \) |
$1.383448027$ |
$1.120257005$ |
4.893407031 |
\( -\frac{1064019559329}{125497034} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -35944\) , \( -2868878\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-35944{x}-2868878$ |
| 26.1-c2 |
26.1-c |
$2$ |
$7$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{14} \cdot 13^{14} \) |
$4.60133$ |
$(2,a), (13,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.6.1 |
$9$ |
\( 2^{2} \) |
$0.197635432$ |
$7.841799039$ |
4.893407031 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -454\) , \( 5812\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-454{x}+5812$ |
| 26.1-d1 |
26.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{30} \cdot 13^{2} \) |
$4.60133$ |
$(2,a), (13,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$7.974205950$ |
$1.793868261$ |
5.018411957 |
\( -\frac{10730978619193}{6656} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -1399\) , \( 49497\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2-1399{x}+49497$ |
| 26.1-d2 |
26.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{18} \cdot 13^{6} \) |
$4.60133$ |
$(2,a), (13,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$2.658068650$ |
$5.381604785$ |
5.018411957 |
\( -\frac{10218313}{17576} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 421\) , \( -1099\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+421{x}-1099$ |
| 26.1-d3 |
26.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{14} \cdot 13^{2} \) |
$4.60133$ |
$(2,a), (13,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$0.886022883$ |
$16.14481435$ |
5.018411957 |
\( \frac{12167}{26} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 441\) , \( -1383\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+441{x}-1383$ |
| 26.1-e1 |
26.1-e |
$3$ |
$9$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{18} \cdot 5^{12} \cdot 13^{2} \) |
$4.60133$ |
$(2,a), (13,a)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1.071599764$ |
$1.793868261$ |
12.13902974 |
\( -\frac{10730978619193}{6656} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -11488\) , \( -478719\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-11488{x}-478719$ |
| 26.1-e2 |
26.1-e |
$3$ |
$9$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{6} \cdot 5^{12} \cdot 13^{6} \) |
$4.60133$ |
$(2,a), (13,a)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$1.071599764$ |
$5.381604785$ |
12.13902974 |
\( -\frac{10218313}{17576} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -113\) , \( -969\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-113{x}-969$ |
| 26.1-e3 |
26.1-e |
$3$ |
$9$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{2} \cdot 5^{12} \cdot 13^{2} \) |
$4.60133$ |
$(2,a), (13,a)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$1.071599764$ |
$16.14481435$ |
12.13902974 |
\( \frac{12167}{26} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 12\) , \( 31\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2+12{x}+31$ |
| 26.1-f1 |
26.1-f |
$2$ |
$7$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{2} \cdot 13^{14} \) |
$4.60133$ |
$(2,a), (13,a)$ |
$0 \le r \le 2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$16$ |
\( 2^{2} \) |
$1$ |
$1.120257005$ |
3.144097249 |
\( -\frac{1064019559329}{125497034} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -213\) , \( -1257\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-213{x}-1257$ |
| 26.1-f2 |
26.1-f |
$2$ |
$7$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{14} \cdot 13^{2} \) |
$4.60133$ |
$(2,a), (13,a)$ |
$0 \le r \le 2$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$16$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$7.841799039$ |
3.144097249 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 26.1-g1 |
26.1-g |
$2$ |
$7$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{14} \cdot 13^{14} \) |
$4.60133$ |
$(2,a), (13,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.6.1 |
$49$ |
\( 2^{2} \cdot 7 \) |
$0.089317794$ |
$1.120257005$ |
12.04032185 |
\( -\frac{1064019559329}{125497034} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -455\) , \( 18287\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-455{x}+18287$ |
| 26.1-g2 |
26.1-g |
$2$ |
$7$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{26} \cdot 13^{2} \) |
$4.60133$ |
$(2,a), (13,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.6.1 |
$1$ |
\( 2^{2} \cdot 7 \) |
$0.625224564$ |
$7.841799039$ |
12.04032185 |
\( -\frac{2146689}{1664} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 385\) , \( -1033\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+385{x}-1033$ |
| 26.1-h1 |
26.1-h |
$3$ |
$9$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{18} \cdot 13^{14} \) |
$4.60133$ |
$(2,a), (13,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$2.010370350$ |
$1.793868261$ |
11.38668853 |
\( -\frac{10730978619193}{6656} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -77659\) , \( -8336303\bigr] \) |
${y}^2+{x}{y}={x}^3-77659{x}-8336303$ |
| 26.1-h2 |
26.1-h |
$3$ |
$9$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{6} \cdot 13^{18} \) |
$4.60133$ |
$(2,a), (13,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.670123450$ |
$5.381604785$ |
11.38668853 |
\( -\frac{10218313}{17576} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -764\) , \( -16264\bigr] \) |
${y}^2+{x}{y}={x}^3-764{x}-16264$ |
| 26.1-h3 |
26.1-h |
$3$ |
$9$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{2} \cdot 13^{14} \) |
$4.60133$ |
$(2,a), (13,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$2.010370350$ |
$16.14481435$ |
11.38668853 |
\( \frac{12167}{26} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 81\) , \( 467\bigr] \) |
${y}^2+{x}{y}={x}^3+81{x}+467$ |
| 32.1-a1 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \cdot 13^{12} \) |
$4.84649$ |
$(2,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$4$ |
\( 2 \) |
$0.949741086$ |
$13.75037163$ |
2.290751511 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 169\) , \( 0\bigr] \) |
${y}^2={x}^3+169{x}$ |
| 32.1-a2 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \cdot 5^{12} \) |
$4.84649$ |
$(2,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1.899482172$ |
$13.75037163$ |
2.290751511 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -25\) , \( 0\bigr] \) |
${y}^2={x}^3-25{x}$ |
| 32.1-a3 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \cdot 13^{12} \) |
$4.84649$ |
$(2,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$4$ |
\( 2 \) |
$0.949741086$ |
$13.75037163$ |
2.290751511 |
\( 287496 \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -69\) , \( -90\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-69{x}-90$ |
| 32.1-a4 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \cdot 13^{12} \) |
$4.84649$ |
$(2,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$3.798964345$ |
$13.75037163$ |
2.290751511 |
\( 287496 \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -134\) , \( 7567\bigr] \) |
${y}^2+a{x}{y}={x}^3+{x}^2-134{x}+7567$ |
| 32.1-b1 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{24} \) |
$4.84649$ |
$(2,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$16$ |
\( 2 \) |
$1$ |
$13.75037163$ |
1.205987371 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4\) , \( 0\bigr] \) |
${y}^2={x}^3+4{x}$ |
| 32.1-b2 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$4.84649$ |
$(2,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$16$ |
\( 2 \) |
$1$ |
$13.75037163$ |
1.205987371 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^3-{x}$ |
| 32.1-b3 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{18} \) |
$4.84649$ |
$(2,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$13.75037163$ |
1.205987371 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -11\) , \( -14\bigr] \) |
${y}^2={x}^3-11{x}-14$ |
| 32.1-b4 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{18} \) |
$4.84649$ |
$(2,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$16$ |
\( 2 \) |
$1$ |
$13.75037163$ |
1.205987371 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -11\) , \( 14\bigr] \) |
${y}^2={x}^3-11{x}+14$ |
| 32.1-c1 |
32.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$4.84649$ |
$(2,a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$4$ |
\( 2 \) |
$2.326779878$ |
$13.75037163$ |
11.22426859 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^3+{x}$ |
| 32.1-c2 |
32.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{24} \) |
$4.84649$ |
$(2,a)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$4$ |
\( 2 \) |
$9.307119513$ |
$13.75037163$ |
11.22426859 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4\) , \( 0\bigr] \) |
${y}^2={x}^3-4{x}$ |
| 32.1-c3 |
32.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$4.84649$ |
$(2,a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$9.307119513$ |
$13.75037163$ |
11.22426859 |
\( 287496 \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 393\) , \( -1098\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+393{x}-1098$ |
| 32.1-c4 |
32.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$4.84649$ |
$(2,a)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$37.22847805$ |
$13.75037163$ |
11.22426859 |
\( 287496 \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 328\) , \( -1127\bigr] \) |
${y}^2+a{x}{y}={x}^3+{x}^2+328{x}-1127$ |
| 32.1-d1 |
32.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \cdot 5^{12} \) |
$4.84649$ |
$(2,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$4$ |
\( 2 \) |
$2.916255868$ |
$13.75037163$ |
7.033935497 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 25\) , \( 0\bigr] \) |
${y}^2={x}^3+25{x}$ |
| 32.1-d2 |
32.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \cdot 13^{12} \) |
$4.84649$ |
$(2,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$5.832511736$ |
$13.75037163$ |
7.033935497 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -169\) , \( 0\bigr] \) |
${y}^2={x}^3-169{x}$ |
*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.
