| 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 |
$2$ |
$19$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
16.1 |
\( 2^{4} \) |
\( 2^{24} \) |
$1.74193$ |
$(2,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-19$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5, 19$ |
5Ns.2.1, 19B.18.6 |
$1$ |
\( 1 \) |
$1$ |
$4.390177367$ |
0.900845388 |
\( -884736 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( -6 a + 16\) , \( 2 a - 64\bigr] \) |
${y}^2+a{y}={x}^3+\left(-6a+16\right){x}+2a-64$ |
| 16.1-a2 |
16.1-a |
$2$ |
$19$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \cdot 3^{12} \) |
$1.74193$ |
$(2,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-19$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5, 19$ |
5Ns.2.1, 19B.18.6 |
$1$ |
\( 1 \) |
$1$ |
$4.390177367$ |
0.900845388 |
\( -884736 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 10 a + 48\) , \( 21 a - 216\bigr] \) |
${y}^2+a{y}={x}^3+\left(10a+48\right){x}+21a-216$ |
| 16.5-a1 |
16.5-a |
$2$ |
$19$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
16.5 |
\( 2^{4} \) |
\( 2^{12} \cdot 3^{12} \) |
$1.74193$ |
$(2,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-19$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5, 19$ |
5Ns.2.1, 19B.18.6 |
$1$ |
\( 1 \) |
$1$ |
$4.390177367$ |
0.900845388 |
\( -884736 \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( -10 a + 58\) , \( -22 a - 195\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^3+\left(-10a+58\right){x}-22a-195$ |
| 16.5-a2 |
16.5-a |
$2$ |
$19$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
16.5 |
\( 2^{4} \) |
\( 2^{24} \) |
$1.74193$ |
$(2,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-19$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5, 19$ |
5Ns.2.1, 19B.18.6 |
$1$ |
\( 1 \) |
$1$ |
$4.390177367$ |
0.900845388 |
\( -884736 \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 6 a + 10\) , \( -3 a - 62\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^3+\left(6a+10\right){x}-3a-62$ |
| 19.1-a1 |
19.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
19.1 |
\( 19 \) |
\( 11^{12} \cdot 19^{2} \) |
$1.81840$ |
$(19,a+9)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$4.071485414$ |
$8.595017252$ |
1.795179324 |
\( \frac{27}{19} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( a - 3\) , \( 21 a - 262\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(a-3\right){x}+21a-262$ |
| 19.1-a2 |
19.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
19.1 |
\( 19 \) |
\( 11^{12} \cdot 19^{4} \) |
$1.81840$ |
$(19,a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$2.035742707$ |
$4.297508626$ |
1.795179324 |
\( \frac{13312053}{361} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -119 a + 212\) , \( 464 a - 5326\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(-119a+212\right){x}+464a-5326$ |
| 19.1-a3 |
19.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
19.1 |
\( 19 \) |
\( 3^{12} \cdot 19 \) |
$1.81840$ |
$(19,a+9)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 1 \) |
$8.142970828$ |
$8.595017252$ |
1.795179324 |
\( \frac{86022}{19} a + \frac{1125603}{19} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -3 a - 1\) , \( -3 a + 16\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(-3a-1\right){x}-3a+16$ |
| 19.1-a4 |
19.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
19.1 |
\( 19 \) |
\( 2^{12} \cdot 19 \) |
$1.81840$ |
$(19,a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 1 \) |
$2.035742707$ |
$8.595017252$ |
1.795179324 |
\( -\frac{86022}{19} a + \frac{1211625}{19} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( 3 a + 13\) , \( -3 a - 10\bigr] \) |
${y}^2+a{x}{y}={x}^3-a{x}^2+\left(3a+13\right){x}-3a-10$ |
| 19.1-b1 |
19.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$1.81840$ |
$(19,a+9)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \) |
$1$ |
$0.935309008$ |
0.383842718 |
\( -\frac{50357871050752}{19} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -769\) , \( -8470\bigr] \) |
${y}^2+{y}={x}^3+{x}^2-769{x}-8470$ |
| 19.1-b2 |
19.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
19.1 |
\( 19 \) |
\( 19^{6} \) |
$1.81840$ |
$(19,a+9)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$2.805927025$ |
0.383842718 |
\( -\frac{89915392}{6859} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -9\) , \( -15\bigr] \) |
${y}^2+{y}={x}^3+{x}^2-9{x}-15$ |
| 19.1-b3 |
19.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$1.81840$ |
$(19,a+9)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \) |
$1$ |
$8.417781075$ |
0.383842718 |
\( \frac{32768}{19} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 1\) , \( 0\bigr] \) |
${y}^2+{y}={x}^3+{x}^2+{x}$ |
| 19.1-c1 |
19.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
19.1 |
\( 19 \) |
\( 5^{12} \cdot 19^{2} \) |
$1.81840$ |
$(19,a+9)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$9$ |
\( 2 \) |
$1$ |
$0.935309008$ |
3.454584462 |
\( -\frac{50357871050752}{19} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -19233\) , \( -1020257\bigr] \) |
${y}^2+{y}={x}^3-{x}^2-19233{x}-1020257$ |
| 19.1-c2 |
19.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
19.1 |
\( 19 \) |
\( 5^{12} \cdot 19^{6} \) |
$1.81840$ |
$(19,a+9)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$2.805927025$ |
3.454584462 |
\( -\frac{89915392}{6859} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -233\) , \( -1382\bigr] \) |
${y}^2+{y}={x}^3-{x}^2-233{x}-1382$ |
| 19.1-c3 |
19.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
19.1 |
\( 19 \) |
\( 5^{12} \cdot 19^{2} \) |
$1.81840$ |
$(19,a+9)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2 \) |
$1$ |
$8.417781075$ |
3.454584462 |
\( \frac{32768}{19} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 17\) , \( -7\bigr] \) |
${y}^2+{y}={x}^3-{x}^2+17{x}-7$ |
| 19.1-d1 |
19.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
19.1 |
\( 19 \) |
\( 11^{12} \cdot 19^{2} \) |
$1.81840$ |
$(19,a+9)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$4.071485414$ |
$8.595017252$ |
1.795179324 |
\( \frac{27}{19} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -2 a - 1\) , \( -22 a - 240\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3-{x}^2+\left(-2a-1\right){x}-22a-240$ |
| 19.1-d2 |
19.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
19.1 |
\( 19 \) |
\( 11^{12} \cdot 19^{4} \) |
$1.81840$ |
$(19,a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$2.035742707$ |
$4.297508626$ |
1.795179324 |
\( \frac{13312053}{361} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 118 a + 94\) , \( -465 a - 4861\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3-{x}^2+\left(118a+94\right){x}-465a-4861$ |
| 19.1-d3 |
19.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
19.1 |
\( 19 \) |
\( 2^{12} \cdot 19 \) |
$1.81840$ |
$(19,a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 1 \) |
$2.035742707$ |
$8.595017252$ |
1.795179324 |
\( \frac{86022}{19} a + \frac{1125603}{19} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -3 a + 16\) , \( 3 a - 13\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3-{x}^2+\left(-3a+16\right){x}+3a-13$ |
| 19.1-d4 |
19.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
19.1 |
\( 19 \) |
\( 3^{12} \cdot 19 \) |
$1.81840$ |
$(19,a+9)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 1 \) |
$8.142970828$ |
$8.595017252$ |
1.795179324 |
\( -\frac{86022}{19} a + \frac{1211625}{19} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 2 a - 3\) , \( 2 a + 14\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3-{x}^2+\left(2a-3\right){x}+2a+14$ |
| 32.2-a1 |
32.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
32.2 |
\( 2^{5} \) |
\( 2^{30} \) |
$2.07151$ |
$(2,a), (2,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Nn |
$1$ |
\( 2^{2} \) |
$1$ |
$4.962388438$ |
4.073042490 |
\( -\frac{27}{8} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( 3 a + 8\) , \( -3 a + 8\bigr] \) |
${y}^2+a{x}{y}={x}^3-a{x}^2+\left(3a+8\right){x}-3a+8$ |
| 32.2-b1 |
32.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
32.2 |
\( 2^{5} \) |
\( 2^{18} \cdot 3^{12} \) |
$2.07151$ |
$(2,a), (2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Nn |
$1$ |
\( 2 \cdot 3 \) |
$0.119785385$ |
$4.962388438$ |
1.463672891 |
\( -\frac{27}{8} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 3 a + 21\) , \( -7 a + 34\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-a{x}^2+\left(3a+21\right){x}-7a+34$ |
| 32.5-a1 |
32.5-a |
$1$ |
$1$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
32.5 |
\( 2^{5} \) |
\( 2^{30} \) |
$2.07151$ |
$(2,a), (2,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Nn |
$1$ |
\( 2^{2} \) |
$1$ |
$4.962388438$ |
4.073042490 |
\( -\frac{27}{8} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -3 a + 11\) , \( 3 a + 5\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3-{x}^2+\left(-3a+11\right){x}+3a+5$ |
| 32.5-b1 |
32.5-b |
$1$ |
$1$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
32.5 |
\( 2^{5} \) |
\( 2^{18} \cdot 3^{12} \) |
$2.07151$ |
$(2,a), (2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Nn |
$1$ |
\( 2 \cdot 3 \) |
$0.119785385$ |
$4.962388438$ |
1.463672891 |
\( -\frac{27}{8} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -5 a + 24\) , \( 6 a + 27\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(-5a+24\right){x}+6a+27$ |
| 36.1-a1 |
36.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{12} \) |
$2.13342$ |
$(2,a), (3,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$0.509647014$ |
$2.894099613$ |
1.210629197 |
\( \frac{90112}{729} a + \frac{8192}{729} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 3 a\) , \( 7 a + 12\bigr] \) |
${y}^2={x}^3+a{x}^2+3a{x}+7a+12$ |
| 36.1-a2 |
36.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 11^{12} \) |
$2.13342$ |
$(2,a), (3,a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1.528941043$ |
$2.894099613$ |
1.210629197 |
\( \frac{630784}{9} a + \frac{352256}{9} \) |
\( \bigl[0\) , \( a\) , \( a\) , \( -141 a + 1872\) , \( -5178 a - 12924\bigr] \) |
${y}^2+a{y}={x}^3+a{x}^2+\left(-141a+1872\right){x}-5178a-12924$ |
| 36.1-b1 |
36.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{24} \) |
$2.13342$ |
$(2,a), (3,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$0.447257231$ |
$2.894099613$ |
3.187280495 |
\( \frac{90112}{729} a + \frac{8192}{729} \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( -6 a + 24\) , \( 21 a + 92\bigr] \) |
${y}^2+a{y}={x}^3+\left(-6a+24\right){x}+21a+92$ |
| 36.1-b2 |
36.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 11^{12} \) |
$2.13342$ |
$(2,a), (3,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1.341771693$ |
$2.894099613$ |
3.187280495 |
\( \frac{630784}{9} a + \frac{352256}{9} \) |
\( \bigl[0\) , \( -a\) , \( a\) , \( 307 a - 1392\) , \( -6155 a + 13836\bigr] \) |
${y}^2+a{y}={x}^3-a{x}^2+\left(307a-1392\right){x}-6155a+13836$ |
| 36.4-a1 |
36.4-a |
$4$ |
$15$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
36.4 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{6} \cdot 11^{12} \) |
$2.13342$ |
$(2,a), (2,a+1), (3,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5B |
$1$ |
\( 3 \cdot 5 \) |
$0.165989829$ |
$3.002483121$ |
3.067972783 |
\( \frac{11177205}{32768} a + \frac{16309945}{4096} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -58 a + 759\) , \( -1506 a - 3013\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(-a-1\right){x}^2+\left(-58a+759\right){x}-1506a-3013$ |
| 36.4-a2 |
36.4-a |
$4$ |
$15$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
36.4 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{18} \) |
$2.13342$ |
$(2,a), (2,a+1), (3,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5B |
$1$ |
\( 1 \) |
$2.489847449$ |
$3.002483121$ |
3.067972783 |
\( -\frac{11177205}{32768} a + \frac{141656765}{32768} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 12 a + 9\) , \( -14 a - 51\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(-a-1\right){x}^2+\left(12a+9\right){x}-14a-51$ |
| 36.4-a3 |
36.4-a |
$4$ |
$15$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
36.4 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 11^{12} \) |
$2.13342$ |
$(2,a), (2,a+1), (3,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5B |
$1$ |
\( 3 \) |
$0.829949149$ |
$3.002483121$ |
3.067972783 |
\( \frac{8045895}{32} a + \frac{33294965}{32} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 252 a + 1779\) , \( 4868 a - 32635\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(-a-1\right){x}^2+\left(252a+1779\right){x}+4868a-32635$ |
| 36.4-a4 |
36.4-a |
$4$ |
$15$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
36.4 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{6} \) |
$2.13342$ |
$(2,a), (2,a+1), (3,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5B |
$1$ |
\( 5 \) |
$0.497969489$ |
$3.002483121$ |
3.067972783 |
\( -\frac{8045895}{32} a + \frac{10335215}{8} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 9 a - 27\) , \( -87 a - 50\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+a{x}^2+\left(9a-27\right){x}-87a-50$ |
| 36.4-b1 |
36.4-b |
$4$ |
$15$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
36.4 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{6} \cdot 11^{12} \) |
$2.13342$ |
$(2,a), (2,a+1), (3,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B.1.1, 5B |
$1$ |
\( 1 \) |
$3.409624464$ |
$3.002483121$ |
4.201315650 |
\( \frac{11177205}{32768} a + \frac{16309945}{4096} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -24 a - 779\) , \( -723 a - 5951\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(a-1\right){x}^2+\left(-24a-779\right){x}-723a-5951$ |
| 36.4-b2 |
36.4-b |
$4$ |
$15$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
36.4 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{28} \cdot 3^{6} \) |
$2.13342$ |
$(2,a), (2,a+1), (3,a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B.1.1, 5B |
$1$ |
\( 3 \cdot 5 \) |
$2.045774678$ |
$3.002483121$ |
4.201315650 |
\( -\frac{11177205}{32768} a + \frac{141656765}{32768} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -5 a + 45\) , \( 6 a - 74\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+\left(-5a+45\right){x}+6a-74$ |
| 36.4-b3 |
36.4-b |
$4$ |
$15$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
36.4 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 11^{12} \) |
$2.13342$ |
$(2,a), (2,a+1), (3,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B.1.1, 5B |
$1$ |
\( 5 \) |
$0.681924892$ |
$3.002483121$ |
4.201315650 |
\( \frac{8045895}{32} a + \frac{33294965}{32} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -24 a - 2264\) , \( -1413 a - 40421\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(a-1\right){x}^2+\left(-24a-2264\right){x}-1413a-40421$ |
| 36.4-b4 |
36.4-b |
$4$ |
$15$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
36.4 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{18} \) |
$2.13342$ |
$(2,a), (2,a+1), (3,a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B.1.1, 5B |
$1$ |
\( 3 \) |
$10.22887339$ |
$3.002483121$ |
4.201315650 |
\( -\frac{8045895}{32} a + \frac{10335215}{8} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -24 a - 119\) , \( -197 a - 57\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(a-1\right){x}^2+\left(-24a-119\right){x}-197a-57$ |
| 36.5-a1 |
36.5-a |
$4$ |
$10$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
36.5 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 11^{12} \) |
$2.13342$ |
$(2,a), (2,a+1), (3,a), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2^{2} \) |
$0.774177867$ |
$8.804485622$ |
2.797325012 |
\( -\frac{24389}{12} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( 15 a + 3\) , \( 35 a + 172\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+a{x}^2+\left(15a+3\right){x}+35a+172$ |
| 36.5-a2 |
36.5-a |
$4$ |
$10$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
36.5 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{10} \cdot 11^{12} \) |
$2.13342$ |
$(2,a), (2,a+1), (3,a), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2^{2} \cdot 5^{2} \) |
$0.154835573$ |
$1.760897124$ |
2.797325012 |
\( -\frac{19465109}{248832} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( 135 a + 98\) , \( -2499 a - 29896\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+a{x}^2+\left(135a+98\right){x}-2499a-29896$ |
| 36.5-a3 |
36.5-a |
$4$ |
$10$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
36.5 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{20} \cdot 11^{12} \) |
$2.13342$ |
$(2,a), (2,a+1), (3,a), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2^{2} \cdot 5^{2} \) |
$0.309671146$ |
$0.880448562$ |
2.797325012 |
\( \frac{502270291349}{1889568} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( 3975 a + 3138\) , \( -83587 a - 992072\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+a{x}^2+\left(3975a+3138\right){x}-83587a-992072$ |
| 36.5-a4 |
36.5-a |
$4$ |
$10$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
36.5 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 11^{12} \) |
$2.13342$ |
$(2,a), (2,a+1), (3,a), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2^{2} \) |
$1.548355734$ |
$4.402242811$ |
2.797325012 |
\( \frac{131872229}{18} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( 255 a + 193\) , \( 1575 a + 13592\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+a{x}^2+\left(255a+193\right){x}+1575a+13592$ |
| 36.5-b1 |
36.5-b |
$4$ |
$10$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
36.5 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 11^{12} \) |
$2.13342$ |
$(2,a), (2,a+1), (3,a), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2^{2} \) |
$0.774177867$ |
$8.804485622$ |
2.797325012 |
\( -\frac{24389}{12} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -15 a + 18\) , \( -35 a + 207\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(-a+1\right){x}^2+\left(-15a+18\right){x}-35a+207$ |
| 36.5-b2 |
36.5-b |
$4$ |
$10$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
36.5 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{10} \cdot 11^{12} \) |
$2.13342$ |
$(2,a), (2,a+1), (3,a), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2^{2} \cdot 5^{2} \) |
$0.154835573$ |
$1.760897124$ |
2.797325012 |
\( -\frac{19465109}{248832} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -135 a + 233\) , \( 2499 a - 32395\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(-a+1\right){x}^2+\left(-135a+233\right){x}+2499a-32395$ |
| 36.5-b3 |
36.5-b |
$4$ |
$10$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
36.5 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{20} \cdot 11^{12} \) |
$2.13342$ |
$(2,a), (2,a+1), (3,a), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2^{2} \cdot 5^{2} \) |
$0.309671146$ |
$0.880448562$ |
2.797325012 |
\( \frac{502270291349}{1889568} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -3975 a + 7113\) , \( 83587 a - 1075659\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(-a+1\right){x}^2+\left(-3975a+7113\right){x}+83587a-1075659$ |
| 36.5-b4 |
36.5-b |
$4$ |
$10$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
36.5 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 11^{12} \) |
$2.13342$ |
$(2,a), (2,a+1), (3,a), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2^{2} \) |
$1.548355734$ |
$4.402242811$ |
2.797325012 |
\( \frac{131872229}{18} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -255 a + 448\) , \( -1575 a + 15167\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(-a+1\right){x}^2+\left(-255a+448\right){x}-1575a+15167$ |
| 36.6-a1 |
36.6-a |
$4$ |
$15$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
36.6 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{28} \cdot 3^{6} \) |
$2.13342$ |
$(2,a), (2,a+1), (3,a+2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B.1.1, 5B |
$1$ |
\( 3 \cdot 5 \) |
$2.045774678$ |
$3.002483121$ |
4.201315650 |
\( \frac{11177205}{32768} a + \frac{16309945}{4096} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 3 a + 40\) , \( -7 a - 68\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-a{x}^2+\left(3a+40\right){x}-7a-68$ |
| 36.6-a2 |
36.6-a |
$4$ |
$15$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
36.6 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{6} \cdot 11^{12} \) |
$2.13342$ |
$(2,a), (2,a+1), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B.1.1, 5B |
$1$ |
\( 1 \) |
$3.409624464$ |
$3.002483121$ |
4.201315650 |
\( -\frac{11177205}{32768} a + \frac{141656765}{32768} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 24 a - 803\) , \( 723 a - 6674\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-a{x}^2+\left(24a-803\right){x}+723a-6674$ |
| 36.6-a3 |
36.6-a |
$4$ |
$15$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
36.6 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{18} \) |
$2.13342$ |
$(2,a), (2,a+1), (3,a+2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B.1.1, 5B |
$1$ |
\( 3 \) |
$10.22887339$ |
$3.002483121$ |
4.201315650 |
\( \frac{8045895}{32} a + \frac{33294965}{32} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 24 a - 143\) , \( 197 a - 254\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-a{x}^2+\left(24a-143\right){x}+197a-254$ |
| 36.6-a4 |
36.6-a |
$4$ |
$15$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
36.6 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 11^{12} \) |
$2.13342$ |
$(2,a), (2,a+1), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B.1.1, 5B |
$1$ |
\( 5 \) |
$0.681924892$ |
$3.002483121$ |
4.201315650 |
\( -\frac{8045895}{32} a + \frac{10335215}{8} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 24 a - 2288\) , \( 1413 a - 41834\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-a{x}^2+\left(24a-2288\right){x}+1413a-41834$ |
| 36.6-b1 |
36.6-b |
$4$ |
$15$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
36.6 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{18} \) |
$2.13342$ |
$(2,a), (2,a+1), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5B |
$1$ |
\( 1 \) |
$2.489847449$ |
$3.002483121$ |
3.067972783 |
\( \frac{11177205}{32768} a + \frac{16309945}{4096} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -10 a + 20\) , \( 3 a - 45\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(a+1\right){x}^2+\left(-10a+20\right){x}+3a-45$ |
| 36.6-b2 |
36.6-b |
$4$ |
$15$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
36.6 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{6} \cdot 11^{12} \) |
$2.13342$ |
$(2,a), (2,a+1), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5B |
$1$ |
\( 3 \cdot 5 \) |
$0.165989829$ |
$3.002483121$ |
3.067972783 |
\( -\frac{11177205}{32768} a + \frac{141656765}{32768} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 60 a + 700\) , \( 1565 a - 3819\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(a+1\right){x}^2+\left(60a+700\right){x}+1565a-3819$ |
| 36.6-b3 |
36.6-b |
$4$ |
$15$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
36.6 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{6} \) |
$2.13342$ |
$(2,a), (2,a+1), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5B |
$1$ |
\( 5 \) |
$0.497969489$ |
$3.002483121$ |
3.067972783 |
\( \frac{8045895}{32} a + \frac{33294965}{32} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -20 a - 30\) , \( 48 a + 211\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(-20a-30\right){x}+48a+211$ |
| 36.6-b4 |
36.6-b |
$4$ |
$15$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
36.6 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 11^{12} \) |
$2.13342$ |
$(2,a), (2,a+1), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5B |
$1$ |
\( 3 \) |
$0.829949149$ |
$3.002483121$ |
3.067972783 |
\( -\frac{8045895}{32} a + \frac{10335215}{8} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -250 a + 2030\) , \( -5119 a - 25737\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(a+1\right){x}^2+\left(-250a+2030\right){x}-5119a-25737$ |
*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.
