| 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 |
| 18.2-a1 |
18.2-a |
$2$ |
$5$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{20} \cdot 41^{12} \) |
$5.00694$ |
$(2,a+1), (3,a+1), (3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$2.140512075$ |
3.147471553 |
\( -\frac{527709995441}{118098} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 4040 a - 277678\) , \( -1324913 a + 55306459\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(a-1\right){x}^2+\left(4040a-277678\right){x}-1324913a+55306459$ |
| 18.2-a2 |
18.2-a |
$2$ |
$5$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{4} \cdot 41^{12} \) |
$5.00694$ |
$(2,a+1), (3,a+1), (3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B |
$1$ |
\( 2^{3} \) |
$1$ |
$10.70256037$ |
3.147471553 |
\( \frac{493039}{288} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -40 a + 2652\) , \( 1023 a - 3421\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(a-1\right){x}^2+\left(-40a+2652\right){x}+1023a-3421$ |
| 18.2-b1 |
18.2-b |
$2$ |
$5$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{20} \cdot 41^{12} \) |
$5.00694$ |
$(2,a+1), (3,a+1), (3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$2.140512075$ |
3.147471553 |
\( -\frac{527709995441}{118098} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 4072 a - 276841\) , \( 1260017 a - 50867477\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+\left(-a-1\right){x}^2+\left(4072a-276841\right){x}+1260017a-50867477$ |
| 18.2-b2 |
18.2-b |
$2$ |
$5$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{4} \cdot 41^{12} \) |
$5.00694$ |
$(2,a+1), (3,a+1), (3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B |
$1$ |
\( 2^{3} \) |
$1$ |
$10.70256037$ |
3.147471553 |
\( \frac{493039}{288} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -8 a + 3489\) , \( -639 a - 42877\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+\left(-a-1\right){x}^2+\left(-8a+3489\right){x}-639a-42877$ |
| 18.2-c1 |
18.2-c |
$2$ |
$5$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{20} \) |
$5.00694$ |
$(2,a+1), (3,a+1), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1.186573303$ |
$2.140512075$ |
7.469411437 |
\( -\frac{527709995441}{118098} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 14 a + 1425\) , \( -719 a - 13199\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+\left(14a+1425\right){x}-719a-13199$ |
| 18.2-c2 |
18.2-c |
$2$ |
$5$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{4} \) |
$5.00694$ |
$(2,a+1), (3,a+1), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.237314660$ |
$10.70256037$ |
7.469411437 |
\( \frac{493039}{288} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 14 a + 745\) , \( -111 a - 2999\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+\left(14a+745\right){x}-111a-2999$ |
| 18.2-d1 |
18.2-d |
$2$ |
$5$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{20} \) |
$5.00694$ |
$(2,a+1), (3,a+1), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1.186573303$ |
$2.140512075$ |
7.469411437 |
\( -\frac{527709995441}{118098} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -16 a + 1425\) , \( 718 a - 13199\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+{x}^2+\left(-16a+1425\right){x}+718a-13199$ |
| 18.2-d2 |
18.2-d |
$2$ |
$5$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{4} \) |
$5.00694$ |
$(2,a+1), (3,a+1), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.237314660$ |
$10.70256037$ |
7.469411437 |
\( \frac{493039}{288} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -16 a + 745\) , \( 110 a - 2999\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+{x}^2+\left(-16a+745\right){x}+110a-2999$ |
| 20.1-a1 |
20.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{16} \cdot 5^{12} \) |
$5.14058$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2 \) |
$1$ |
$4.282063771$ |
0.314823589 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -36\) , \( -140\bigr] \) |
${y}^2={x}^3+{x}^2-36{x}-140$ |
| 20.1-a2 |
20.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{16} \cdot 5^{4} \) |
$5.14058$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$12.84619131$ |
0.314823589 |
\( \frac{21296}{25} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 4\) , \( 4\bigr] \) |
${y}^2={x}^3+{x}^2+4{x}+4$ |
| 20.1-a3 |
20.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$5.14058$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$12.84619131$ |
0.314823589 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^3+{x}^2-{x}$ |
| 20.1-a4 |
20.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{6} \) |
$5.14058$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2 \) |
$1$ |
$4.282063771$ |
0.314823589 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -41\) , \( -116\bigr] \) |
${y}^2={x}^3+{x}^2-41{x}-116$ |
| 20.1-b1 |
20.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{12} \cdot 41^{12} \) |
$5.14058$ |
$(2,a+1), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1.575017980$ |
$4.282063771$ |
4.462675330 |
\( -\frac{20720464}{15625} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -266 a + 15668\) , \( -66322 a - 534594\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a-1\right){x}^2+\left(-266a+15668\right){x}-66322a-534594$ |
| 20.1-b2 |
20.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{4} \cdot 41^{12} \) |
$5.14058$ |
$(2,a+1), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$4.725053941$ |
$12.84619131$ |
4.462675330 |
\( \frac{21296}{25} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -26 a - 822\) , \( 906 a + 26844\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a-1\right){x}^2+\left(-26a-822\right){x}+906a+26844$ |
| 20.1-b3 |
20.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{14} \) |
$5.14058$ |
$(2,a+1), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$9.450107883$ |
$12.84619131$ |
4.462675330 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -33\) , \( -62\bigr] \) |
${y}^2={x}^3+{x}^2-33{x}-62$ |
| 20.1-b4 |
20.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{18} \) |
$5.14058$ |
$(2,a+1), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3^{2} \) |
$3.150035961$ |
$4.282063771$ |
4.462675330 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1033\) , \( 12438\bigr] \) |
${y}^2={x}^3+{x}^2-1033{x}+12438$ |
| 20.1-c1 |
20.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{16} \cdot 5^{12} \) |
$5.14058$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$36$ |
\( 2 \) |
$1$ |
$4.282063771$ |
2.833412307 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -36\) , \( 140\bigr] \) |
${y}^2={x}^3-{x}^2-36{x}+140$ |
| 20.1-c2 |
20.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{16} \cdot 5^{4} \) |
$5.14058$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$12.84619131$ |
2.833412307 |
\( \frac{21296}{25} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 4\) , \( -4\bigr] \) |
${y}^2={x}^3-{x}^2+4{x}-4$ |
| 20.1-c3 |
20.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$5.14058$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$12.84619131$ |
2.833412307 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^3-{x}^2-{x}$ |
| 20.1-c4 |
20.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{6} \) |
$5.14058$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$36$ |
\( 2 \) |
$1$ |
$4.282063771$ |
2.833412307 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -41\) , \( 116\bigr] \) |
${y}^2={x}^3-{x}^2-41{x}+116$ |
| 20.1-d1 |
20.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{12} \cdot 41^{12} \) |
$5.14058$ |
$(2,a+1), (5,a)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
|
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$4.282063771$ |
12.53542348 |
\( -\frac{20720464}{15625} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -265 a + 15637\) , \( 88732 a + 107536\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+a{x}^2+\left(-265a+15637\right){x}+88732a+107536$ |
| 20.1-d2 |
20.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{4} \cdot 41^{12} \) |
$5.14058$ |
$(2,a+1), (5,a)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
|
\( 2^{2} \) |
$1$ |
$12.84619131$ |
12.53542348 |
\( \frac{21296}{25} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -25 a - 853\) , \( -2426 a + 12888\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+a{x}^2+\left(-25a-853\right){x}-2426a+12888$ |
| 20.1-d3 |
20.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{14} \) |
$5.14058$ |
$(2,a+1), (5,a)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
|
\( 2 \) |
$1$ |
$12.84619131$ |
12.53542348 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -33\) , \( 62\bigr] \) |
${y}^2={x}^3-{x}^2-33{x}+62$ |
| 20.1-d4 |
20.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{18} \) |
$5.14058$ |
$(2,a+1), (5,a)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
|
\( 2 \cdot 3^{2} \) |
$1$ |
$4.282063771$ |
12.53542348 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -1033\) , \( -12438\bigr] \) |
${y}^2={x}^3-{x}^2-1033{x}-12438$ |
| 25.1-a1 |
25.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \cdot 41^{12} \) |
$5.43550$ |
$(5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Nn, 5B |
$1$ |
\( 2 \) |
$1.941017520$ |
$11.78714714$ |
3.364203762 |
\( 4096 \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( 40 a - 2810\) , \( -1845 a + 39081\bigr] \) |
${y}^2+{y}={x}^3+a{x}^2+\left(40a-2810\right){x}-1845a+39081$ |
| 25.1-a2 |
25.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \cdot 41^{12} \) |
$5.43550$ |
$(5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Nn, 5B |
$1$ |
\( 2 \) |
$9.705087602$ |
$2.357429429$ |
3.364203762 |
\( 38477541376 \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( 8440 a - 579960\) , \( 3523425 a - 168000119\bigr] \) |
${y}^2+{y}={x}^3+a{x}^2+\left(8440a-579960\right){x}+3523425a-168000119$ |
| 25.1-b1 |
25.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \cdot 41^{12} \) |
$5.43550$ |
$(5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Nn, 5B |
$1$ |
\( 2 \) |
$1.941017520$ |
$11.78714714$ |
3.364203762 |
\( 4096 \) |
\( \bigl[0\) , \( -a\) , \( a\) , \( 40 a - 2810\) , \( 1845 a - 39035\bigr] \) |
${y}^2+a{y}={x}^3-a{x}^2+\left(40a-2810\right){x}+1845a-39035$ |
| 25.1-b2 |
25.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \cdot 41^{12} \) |
$5.43550$ |
$(5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Nn, 5B |
$1$ |
\( 2 \) |
$9.705087602$ |
$2.357429429$ |
3.364203762 |
\( 38477541376 \) |
\( \bigl[0\) , \( -a\) , \( a\) , \( 8440 a - 579960\) , \( -3523425 a + 168000165\bigr] \) |
${y}^2+a{y}={x}^3-a{x}^2+\left(8440a-579960\right){x}-3523425a+168000165$ |
| 25.1-c1 |
25.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
25.1 |
\( 5^{2} \) |
\( 2^{12} \cdot 5^{18} \) |
$5.43550$ |
$(5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Ns |
$1$ |
\( 2 \) |
$6.111603298$ |
$2.313848657$ |
2.079381795 |
\( \frac{89915392}{15625} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 125\) , \( -5 a\bigr] \) |
${y}^2={x}^3+a{x}^2+125{x}-5a$ |
| 25.1-d1 |
25.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
25.1 |
\( 5^{2} \) |
\( 5^{18} \cdot 41^{12} \) |
$5.43550$ |
$(5,a)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Ns |
|
\( 2 \) |
$1$ |
$2.313848657$ |
5.069464571 |
\( \frac{89915392}{15625} \) |
\( \bigl[0\) , \( a\) , \( a\) , \( 1120 a - 77015\) , \( -175950 a + 6703290\bigr] \) |
${y}^2+a{y}={x}^3+a{x}^2+\left(1120a-77015\right){x}-175950a+6703290$ |
| 25.1-e1 |
25.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
25.1 |
\( 5^{2} \) |
\( 2^{12} \cdot 5^{18} \) |
$5.43550$ |
$(5,a)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Ns |
|
\( 2 \) |
$1$ |
$2.313848657$ |
2.079381795 |
\( \frac{89915392}{15625} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 125\) , \( 5 a\bigr] \) |
${y}^2={x}^3-a{x}^2+125{x}+5a$ |
| 25.1-f1 |
25.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
25.1 |
\( 5^{2} \) |
\( 5^{18} \cdot 41^{12} \) |
$5.43550$ |
$(5,a)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Ns |
|
\( 2 \) |
$1$ |
$2.313848657$ |
5.069464571 |
\( \frac{89915392}{15625} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( 1120 a - 77015\) , \( 175950 a - 6703244\bigr] \) |
${y}^2+{y}={x}^3-a{x}^2+\left(1120a-77015\right){x}+175950a-6703244$ |
| 25.1-g1 |
25.1-g |
$2$ |
$5$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
25.1 |
\( 5^{2} \) |
\( 2^{12} \cdot 5^{6} \) |
$5.43550$ |
$(5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Nn, 5B |
$1$ |
\( 2 \) |
$3.877867907$ |
$11.78714714$ |
6.721184978 |
\( 4096 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -55\) , \( -5 a\bigr] \) |
${y}^2={x}^3+a{x}^2-55{x}-5a$ |
| 25.1-g2 |
25.1-g |
$2$ |
$5$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
25.1 |
\( 5^{2} \) |
\( 2^{12} \cdot 5^{6} \) |
$5.43550$ |
$(5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Nn, 5B |
$1$ |
\( 2 \) |
$19.38933953$ |
$2.357429429$ |
6.721184978 |
\( 38477541376 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 1345\) , \( 1955 a\bigr] \) |
${y}^2={x}^3+a{x}^2+1345{x}+1955a$ |
| 25.1-h1 |
25.1-h |
$2$ |
$5$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
25.1 |
\( 5^{2} \) |
\( 2^{12} \cdot 5^{6} \) |
$5.43550$ |
$(5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Nn, 5B |
$1$ |
\( 2 \) |
$3.877867907$ |
$11.78714714$ |
6.721184978 |
\( 4096 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -55\) , \( 5 a\bigr] \) |
${y}^2={x}^3-a{x}^2-55{x}+5a$ |
| 25.1-h2 |
25.1-h |
$2$ |
$5$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
25.1 |
\( 5^{2} \) |
\( 2^{12} \cdot 5^{6} \) |
$5.43550$ |
$(5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Nn, 5B |
$1$ |
\( 2 \) |
$19.38933953$ |
$2.357429429$ |
6.721184978 |
\( 38477541376 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 1345\) , \( -1955 a\bigr] \) |
${y}^2={x}^3-a{x}^2+1345{x}-1955a$ |
| 36.2-a1 |
36.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
36.2 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{26} \) |
$5.95429$ |
$(2,a+1), (3,a+1), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 3 \) |
$0.948312913$ |
$4.359633269$ |
0.911878578 |
\( \frac{1145801692}{1594323} a + \frac{4425951008}{1594323} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -25 a + 671\) , \( 228 a - 2427\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(-25a+671\right){x}+228a-2427$ |
| 36.2-b1 |
36.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
36.2 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{26} \) |
$5.95429$ |
$(2,a+1), (3,a+1), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 3 \cdot 13 \) |
$0.703548277$ |
$4.359633269$ |
8.794731907 |
\( -\frac{1145801692}{1594323} a + \frac{4425951008}{1594323} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -7 a + 794\) , \( -67 a - 3913\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(-7a+794\right){x}-67a-3913$ |
| 36.2-c1 |
36.2-c |
$1$ |
$1$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
36.2 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{14} \cdot 19^{12} \) |
$5.95429$ |
$(2,a+1), (3,a+1), (3,a+2)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
|
\( 1 \) |
$1$ |
$4.359633269$ |
7.126298801 |
\( \frac{1145801692}{1594323} a + \frac{4425951008}{1594323} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 302 a + 4286\) , \( -2316 a - 191262\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(-a+1\right){x}^2+\left(302a+4286\right){x}-2316a-191262$ |
| 36.2-d1 |
36.2-d |
$1$ |
$1$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
36.2 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{14} \cdot 19^{12} \) |
$5.95429$ |
$(2,a+1), (3,a+1), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 13 \) |
$2.973964267$ |
$4.359633269$ |
12.39205100 |
\( -\frac{1145801692}{1594323} a + \frac{4425951008}{1594323} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -272 a + 4286\) , \( 6294 a + 76182\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(-a+1\right){x}^2+\left(-272a+4286\right){x}+6294a+76182$ |
| 36.2-e1 |
36.2-e |
$1$ |
$1$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
36.2 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{26} \) |
$5.95429$ |
$(2,a+1), (3,a+1), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 3 \) |
$0.948312913$ |
$4.359633269$ |
0.911878578 |
\( -\frac{1145801692}{1594323} a + \frac{4425951008}{1594323} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 25 a + 671\) , \( -228 a - 2427\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3-a{x}^2+\left(25a+671\right){x}-228a-2427$ |
| 36.2-f1 |
36.2-f |
$1$ |
$1$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
36.2 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{26} \) |
$5.95429$ |
$(2,a+1), (3,a+1), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 3 \cdot 13 \) |
$0.703548277$ |
$4.359633269$ |
8.794731907 |
\( \frac{1145801692}{1594323} a + \frac{4425951008}{1594323} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 5 a + 794\) , \( 66 a - 3913\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(5a+794\right){x}+66a-3913$ |
| 36.2-g1 |
36.2-g |
$1$ |
$1$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
36.2 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{14} \cdot 19^{12} \) |
$5.95429$ |
$(2,a+1), (3,a+1), (3,a+2)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
|
\( 1 \) |
$1$ |
$4.359633269$ |
7.126298801 |
\( -\frac{1145801692}{1594323} a + \frac{4425951008}{1594323} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -302 a + 4286\) , \( 2316 a - 191262\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+{x}^2+\left(-302a+4286\right){x}+2316a-191262$ |
| 36.2-h1 |
36.2-h |
$1$ |
$1$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
36.2 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{14} \cdot 19^{12} \) |
$5.95429$ |
$(2,a+1), (3,a+1), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 13 \) |
$2.973964267$ |
$4.359633269$ |
12.39205100 |
\( \frac{1145801692}{1594323} a + \frac{4425951008}{1594323} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 272 a + 4286\) , \( -6294 a + 76182\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+{x}^2+\left(272a+4286\right){x}-6294a+76182$ |
| 37.1-a1 |
37.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
37.1 |
\( 37 \) |
\( 37^{2} \) |
$5.99522$ |
$(37,a)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.365162553$ |
$14.67626548$ |
3.152143043 |
\( \frac{110592}{37} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{y}={x}^3-{x}$ |
| 37.1-b1 |
37.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
37.1 |
\( 37 \) |
\( 37^{2} \) |
$5.99522$ |
$(37,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$4$ |
\( 2 \) |
$1.396151596$ |
$14.67626548$ |
12.05180952 |
\( \frac{110592}{37} \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( -1\) , \( 46\bigr] \) |
${y}^2+a{y}={x}^3-{x}+46$ |
| 37.1-c1 |
37.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
37.1 |
\( 37 \) |
\( 37^{6} \) |
$5.99522$ |
$(37,a)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2 \cdot 3 \) |
$2.031360038$ |
$3.848164764$ |
6.896614407 |
\( \frac{1404928000}{50653} \) |
\( \bigl[0\) , \( -1\) , \( a\) , \( -23\) , \( 96\bigr] \) |
${y}^2+a{y}={x}^3-{x}^2-23{x}+96$ |
| 37.1-c2 |
37.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
37.1 |
\( 37 \) |
\( 37^{2} \) |
$5.99522$ |
$(37,a)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2 \) |
$2.031360038$ |
$11.54449429$ |
6.896614407 |
\( \frac{4096000}{37} \) |
\( \bigl[0\) , \( -1\) , \( a\) , \( -3\) , \( 45\bigr] \) |
${y}^2+a{y}={x}^3-{x}^2-3{x}+45$ |
| 37.1-c3 |
37.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
37.1 |
\( 37 \) |
\( 37^{2} \) |
$5.99522$ |
$(37,a)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2 \) |
$18.28224034$ |
$1.282721588$ |
6.896614407 |
\( \frac{727057727488000}{37} \) |
\( \bigl[0\) , \( -1\) , \( a\) , \( -1873\) , \( 31879\bigr] \) |
${y}^2+a{y}={x}^3-{x}^2-1873{x}+31879$ |
| 37.1-d1 |
37.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
37.1 |
\( 37 \) |
\( 5^{12} \cdot 37^{6} \) |
$5.99522$ |
$(37,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$4$ |
\( 2 \) |
$0.948950578$ |
$3.848164764$ |
2.147837281 |
\( \frac{1404928000}{50653} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -583\) , \( -5057\bigr] \) |
${y}^2+{y}={x}^3-{x}^2-583{x}-5057$ |
*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.
