| 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 |
| 50.1-a1 |
50.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{24} \cdot 5^{8} \) |
$1.84059$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.368666483$ |
1.127984835 |
\( -\frac{1860867}{320} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -2 a - 55\) , \( 49 a - 53\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a-55\right){x}+49a-53$ |
| 50.1-a2 |
50.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{12} \) |
$1.84059$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.368666483$ |
1.127984835 |
\( \frac{804357}{500} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 80 a + 310\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(80a+310\right){x}$ |
| 50.1-a3 |
50.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{2} \cdot 5^{18} \) |
$1.84059$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.368666483$ |
1.127984835 |
\( \frac{57960603}{31250} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( -320 a - 1240\) , \( -2440 a - 9450\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-320a-1240\right){x}-2440a-9450$ |
| 50.1-a4 |
50.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{18} \cdot 5^{10} \) |
$1.84059$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.368666483$ |
1.127984835 |
\( \frac{8527173507}{200} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -2 a - 855\) , \( 2609 a - 853\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a-855\right){x}+2609a-853$ |
| 50.1-b1 |
50.1-b |
$4$ |
$15$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{18} \cdot 5^{8} \) |
$1.84059$ |
$(2,a+1), (5,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B, 5B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.508604290$ |
1.181889568 |
\( -\frac{349938025}{8} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -4016 a - 15563\) , \( -282098 a - 1092579\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-4016a-15563\right){x}-282098a-1092579$ |
| 50.1-b2 |
50.1-b |
$4$ |
$15$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{10} \cdot 5^{4} \) |
$1.84059$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B, 5B.1.1 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$22.88719308$ |
1.181889568 |
\( -\frac{121945}{32} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -3\) , \( 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-3{x}+1$ |
| 50.1-b3 |
50.1-b |
$4$ |
$15$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{14} \cdot 5^{8} \) |
$1.84059$ |
$(2,a+1), (5,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B, 5B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$4.577438616$ |
1.181889568 |
\( -\frac{25}{2} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -16 a - 63\) , \( -898 a - 3479\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-16a-63\right){x}-898a-3479$ |
| 50.1-b4 |
50.1-b |
$4$ |
$15$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{30} \cdot 5^{4} \) |
$1.84059$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B, 5B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \cdot 5 \) |
$1$ |
$2.543021453$ |
1.181889568 |
\( \frac{46969655}{32768} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 22\) , \( -9\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+22{x}-9$ |
| 50.1-c1 |
50.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{24} \cdot 5^{8} \) |
$1.84059$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.368666483$ |
1.127984835 |
\( -\frac{1860867}{320} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 25421 a - 98447\) , \( -4935742 a + 19116051\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(25421a-98447\right){x}-4935742a+19116051$ |
| 50.1-c2 |
50.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{12} \) |
$1.84059$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.368666483$ |
1.127984835 |
\( \frac{804357}{500} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -80 a + 310\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-80a+310\right){x}$ |
| 50.1-c3 |
50.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{2} \cdot 5^{18} \) |
$1.84059$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.368666483$ |
1.127984835 |
\( \frac{57960603}{31250} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( 320 a - 1240\) , \( 2440 a - 9450\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(320a-1240\right){x}+2440a-9450$ |
| 50.1-c4 |
50.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{18} \cdot 5^{10} \) |
$1.84059$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.368666483$ |
1.127984835 |
\( \frac{8527173507}{200} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 422221 a - 1635247\) , \( -293740702 a + 1137652851\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(422221a-1635247\right){x}-293740702a+1137652851$ |
| 50.1-d1 |
50.1-d |
$4$ |
$15$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{18} \cdot 5^{8} \) |
$1.84059$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B.1.1, 5B.4.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$15.95150461$ |
4.118660781 |
\( -\frac{349938025}{8} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -4018 a - 15558\) , \( 270048 a + 1045892\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-4018a-15558\right){x}+270048a+1045892$ |
| 50.1-d2 |
50.1-d |
$4$ |
$15$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{10} \cdot 5^{4} \) |
$1.84059$ |
$(2,a+1), (5,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B.1.2, 5B.4.1 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$3.190300923$ |
4.118660781 |
\( -\frac{121945}{32} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -3\) , \( -7\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-3{x}-7$ |
| 50.1-d3 |
50.1-d |
$4$ |
$15$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{14} \cdot 5^{8} \) |
$1.84059$ |
$(2,a+1), (5,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B.1.2, 5B.4.2 |
$1$ |
\( 2 \) |
$1$ |
$15.95150461$ |
4.118660781 |
\( -\frac{25}{2} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -18 a - 58\) , \( 848 a + 3292\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-18a-58\right){x}+848a+3292$ |
| 50.1-d4 |
50.1-d |
$4$ |
$15$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{30} \cdot 5^{4} \) |
$1.84059$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B.1.1, 5B.4.1 |
$1$ |
\( 2 \cdot 3^{2} \cdot 5 \) |
$1$ |
$3.190300923$ |
4.118660781 |
\( \frac{46969655}{32768} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 22\) , \( 53\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+22{x}+53$ |
| 50.1-e1 |
50.1-e |
$4$ |
$15$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{6} \cdot 5^{8} \) |
$1.84059$ |
$(2,a+1), (5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B, 5B.4.2 |
$1$ |
\( 2 \) |
$0.194697629$ |
$15.95150461$ |
1.603786982 |
\( -\frac{349938025}{8} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -123\) , \( 427\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-123{x}+427$ |
| 50.1-e2 |
50.1-e |
$4$ |
$15$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{22} \cdot 5^{4} \) |
$1.84059$ |
$(2,a+1), (5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B, 5B.4.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.324496049$ |
$3.190300923$ |
1.603786982 |
\( -\frac{121945}{32} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 95 a - 365\) , \( 1450 a - 5615\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(95a-365\right){x}+1450a-5615$ |
| 50.1-e3 |
50.1-e |
$4$ |
$15$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{2} \cdot 5^{8} \) |
$1.84059$ |
$(2,a+1), (5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B, 5B.4.2 |
$1$ |
\( 2 \cdot 3 \) |
$0.064899209$ |
$15.95150461$ |
1.603786982 |
\( -\frac{25}{2} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 2\) , \( 2\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+2{x}+2$ |
| 50.1-e4 |
50.1-e |
$4$ |
$15$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{42} \cdot 5^{4} \) |
$1.84059$ |
$(2,a+1), (5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B, 5B.4.1 |
$1$ |
\( 2 \) |
$0.973488147$ |
$3.190300923$ |
1.603786982 |
\( \frac{46969655}{32768} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -705 a + 2735\) , \( -10690 a + 41405\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-705a+2735\right){x}-10690a+41405$ |
| 50.1-f1 |
50.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{8} \) |
$1.84059$ |
$(2,a+1), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.299193906$ |
$4.368666483$ |
4.049834279 |
\( -\frac{1860867}{320} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 102 a - 392\) , \( -1424 a + 5516\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(102a-392\right){x}-1424a+5516$ |
| 50.1-f2 |
50.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{12} \) |
$1.84059$ |
$(2,a+1), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.897581720$ |
$4.368666483$ |
4.049834279 |
\( \frac{804357}{500} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -2 a + 35\) , \( -a + 37\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a+35\right){x}-a+37$ |
| 50.1-f3 |
50.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{14} \cdot 5^{18} \) |
$1.84059$ |
$(2,a+1), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1.795163441$ |
$4.368666483$ |
4.049834279 |
\( \frac{57960603}{31250} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -2 a - 165\) , \( 79 a - 163\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a-165\right){x}+79a-163$ |
| 50.1-f4 |
50.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{6} \cdot 5^{10} \) |
$1.84059$ |
$(2,a+1), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.598387813$ |
$4.368666483$ |
4.049834279 |
\( \frac{8527173507}{200} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 1702 a - 6592\) , \( -77904 a + 301716\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(1702a-6592\right){x}-77904a+301716$ |
| 50.1-g1 |
50.1-g |
$4$ |
$15$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{6} \cdot 5^{8} \) |
$1.84059$ |
$(2,a+1), (5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B.1.2, 5B.1.3 |
$1$ |
\( 2 \) |
$9.990411618$ |
$0.508604290$ |
2.623902950 |
\( -\frac{349938025}{8} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -126\) , \( -552\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-126{x}-552$ |
| 50.1-g2 |
50.1-g |
$4$ |
$15$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{22} \cdot 5^{4} \) |
$1.84059$ |
$(2,a+1), (5,a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B.1.1, 5B.1.4 |
$1$ |
\( 2 \cdot 3 \) |
$0.666027441$ |
$22.88719308$ |
2.623902950 |
\( -\frac{121945}{32} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 97 a - 376\) , \( -1161 a + 4498\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(97a-376\right){x}-1161a+4498$ |
| 50.1-g3 |
50.1-g |
$4$ |
$15$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{2} \cdot 5^{8} \) |
$1.84059$ |
$(2,a+1), (5,a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B.1.1, 5B.1.3 |
$1$ |
\( 2 \cdot 3 \) |
$3.330137206$ |
$4.577438616$ |
2.623902950 |
\( -\frac{25}{2} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( -2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}-2$ |
| 50.1-g4 |
50.1-g |
$4$ |
$15$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{42} \cdot 5^{4} \) |
$1.84059$ |
$(2,a+1), (5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B.1.2, 5B.1.4 |
$1$ |
\( 2 \) |
$1.998082323$ |
$2.543021453$ |
2.623902950 |
\( \frac{46969655}{32768} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -703 a + 2724\) , \( 8579 a - 33222\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-703a+2724\right){x}+8579a-33222$ |
| 50.1-h1 |
50.1-h |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{8} \) |
$1.84059$ |
$(2,a+1), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.299193906$ |
$4.368666483$ |
4.049834279 |
\( -\frac{1860867}{320} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 100 a - 395\) , \( 1525 a - 5910\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(100a-395\right){x}+1525a-5910$ |
| 50.1-h2 |
50.1-h |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{12} \) |
$1.84059$ |
$(2,a+1), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.897581720$ |
$4.368666483$ |
4.049834279 |
\( \frac{804357}{500} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 35\) , \( 37\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+35{x}+37$ |
| 50.1-h3 |
50.1-h |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{14} \cdot 5^{18} \) |
$1.84059$ |
$(2,a+1), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1.795163441$ |
$4.368666483$ |
4.049834279 |
\( \frac{57960603}{31250} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -165\) , \( -80 a - 163\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}-165{x}-80a-163$ |
| 50.1-h4 |
50.1-h |
$4$ |
$6$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{6} \cdot 5^{10} \) |
$1.84059$ |
$(2,a+1), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.598387813$ |
$4.368666483$ |
4.049834279 |
\( \frac{8527173507}{200} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 1700 a - 6595\) , \( 79605 a - 308310\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(1700a-6595\right){x}+79605a-308310$ |
*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.
