| 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 |
| 9.1-a1 |
9.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$1.18884$ |
$(3,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 5$ |
2Cn, 5B |
$1$ |
\( 1 \) |
$1$ |
$7.349120199$ |
1.913547910 |
\( 1785 a - 671 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -6 a - 2\) , \( -a + 23\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a-1\right){x}^2+\left(-6a-2\right){x}-a+23$ |
| 9.1-a2 |
9.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
9.1 |
\( 3^{2} \) |
\( 3^{18} \) |
$1.18884$ |
$(3,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 5$ |
2Cn, 5B |
$1$ |
\( 1 \) |
$1$ |
$7.349120199$ |
1.913547910 |
\( -1785 a + 1114 \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 4 a + 3\) , \( 23\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-a{x}^2+\left(4a+3\right){x}+23$ |
| 9.3-a1 |
9.3-a |
$2$ |
$5$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
9.3 |
\( 3^{2} \) |
\( 3^{18} \) |
$1.18884$ |
$(3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 5$ |
2Cn, 5B |
$1$ |
\( 1 \) |
$1$ |
$7.349120199$ |
1.913547910 |
\( 1785 a - 671 \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -6 a + 7\) , \( -a + 23\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(-6a+7\right){x}-a+23$ |
| 9.3-a2 |
9.3-a |
$2$ |
$5$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
9.3 |
\( 3^{2} \) |
\( 3^{6} \) |
$1.18884$ |
$(3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 5$ |
2Cn, 5B |
$1$ |
\( 1 \) |
$1$ |
$7.349120199$ |
1.913547910 |
\( -1785 a + 1114 \) |
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( -2 a - 6\) , \( -a + 4\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3+\left(a+1\right){x}^2+\left(-2a-6\right){x}-a+4$ |
| 17.1-a1 |
17.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
17.1 |
\( 17 \) |
\( 3^{12} \cdot 17^{2} \) |
$1.39372$ |
$(a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cn, 3B.1.1 |
$1$ |
\( 2 \) |
$2.529902187$ |
$8.204550500$ |
2.402038670 |
\( -\frac{257085}{289} a + \frac{481258}{289} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -a - 4\) , \( -2 a + 4\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+\left(a+1\right){x}^2+\left(-a-4\right){x}-2a+4$ |
| 17.1-a2 |
17.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
17.1 |
\( 17 \) |
\( 3^{12} \cdot 17^{6} \) |
$1.39372$ |
$(a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cn, 3B.1.1 |
$1$ |
\( 2 \) |
$0.843300729$ |
$2.734850166$ |
2.402038670 |
\( -\frac{25082343195}{24137569} a + \frac{1126875588853}{24137569} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 4 a + 111\) , \( 156 a - 331\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+\left(a+1\right){x}^2+\left(4a+111\right){x}+156a-331$ |
| 17.2-a1 |
17.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
17.2 |
\( 17 \) |
\( 3^{12} \cdot 17^{2} \) |
$1.39372$ |
$(a-2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cn, 3B.1.1 |
$1$ |
\( 2 \) |
$2.529902187$ |
$8.204550500$ |
2.402038670 |
\( \frac{257085}{289} a + \frac{224173}{289} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -6 a - 14\) , \( -4 a + 34\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(a-1\right){x}^2+\left(-6a-14\right){x}-4a+34$ |
| 17.2-a2 |
17.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
17.2 |
\( 17 \) |
\( 3^{12} \cdot 17^{6} \) |
$1.39372$ |
$(a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cn, 3B.1.1 |
$1$ |
\( 2 \) |
$0.843300729$ |
$2.734850166$ |
2.402038670 |
\( \frac{25082343195}{24137569} a + \frac{1101793245658}{24137569} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -11 a + 106\) , \( -42 a - 188\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(a-1\right){x}^2+\left(-11a+106\right){x}-42a-188$ |
| 27.2-a1 |
27.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{21} \) |
$1.56461$ |
$(3,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$3.995286149$ |
3.120851717 |
\( \frac{112132825}{729} a - \frac{38677196}{243} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 12 a - 53\) , \( -105 a + 174\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(12a-53\right){x}-105a+174$ |
| 27.2-a2 |
27.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{18} \) |
$1.56461$ |
$(3,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$7.990572299$ |
3.120851717 |
\( -\frac{2989}{27} a + \frac{1097}{9} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -3 a + 7\) , \( -3 a + 9\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(-3a+7\right){x}-3a+9$ |
| 27.3-a1 |
27.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{21} \) |
$1.56461$ |
$(3,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$3.995286149$ |
3.120851717 |
\( -\frac{112132825}{729} a - \frac{3898763}{729} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -14 a - 39\) , \( 104 a + 70\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-a{x}^2+\left(-14a-39\right){x}+104a+70$ |
| 27.3-a2 |
27.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{18} \) |
$1.56461$ |
$(3,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$7.990572299$ |
3.120851717 |
\( \frac{2989}{27} a + \frac{302}{27} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( a + 6\) , \( 2 a + 7\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-a{x}^2+\left(a+6\right){x}+2a+7$ |
| 36.1-a1 |
36.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{24} \) |
$1.68128$ |
$(3,a), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$3.273009913$ |
1.704438384 |
\( -\frac{423619}{5832} a + \frac{217981}{5832} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -2 a - 30\) , \( -40 a + 68\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a-1\right){x}^2+\left(-2a-30\right){x}-40a+68$ |
| 36.1-b1 |
36.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{18} \) |
$1.68128$ |
$(3,a), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$0.367432411$ |
$5.235122741$ |
2.003402969 |
\( \frac{81375}{2} a - 80875 \) |
\( \bigl[a + 1\) , \( -1\) , \( a\) , \( -4 a - 27\) , \( -4 a + 157\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^3-{x}^2+\left(-4a-27\right){x}-4a+157$ |
| 36.1-b2 |
36.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{6} \) |
$1.68128$ |
$(3,a), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$3.306891705$ |
$5.235122741$ |
2.003402969 |
\( -\frac{81375}{2} a - \frac{80375}{2} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( -a\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3-a{x}$ |
| 36.1-b3 |
36.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{18} \) |
$1.68128$ |
$(3,a), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1.102297235$ |
$5.235122741$ |
2.003402969 |
\( -\frac{42875}{8} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( 4 a\) , \( -14 a - 22\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3+4a{x}-14a-22$ |
| 36.1-c1 |
36.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{18} \) |
$1.68128$ |
$(3,a), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cn, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$2.229782782$ |
$2.002926308$ |
3.100989179 |
\( \frac{2352637}{4096} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -20 a + 21\) , \( -49 a - 174\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(-20a+21\right){x}-49a-174$ |
| 36.1-c2 |
36.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{18} \) |
$1.68128$ |
$(3,a), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cn, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$0.743260927$ |
$2.002926308$ |
3.100989179 |
\( \frac{327638535}{16} a + \frac{42294941}{8} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 126 a + 301\) , \( -306 a + 4947\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(126a+301\right){x}-306a+4947$ |
| 36.1-c3 |
36.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{6} \) |
$1.68128$ |
$(3,a), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cn, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$6.689348348$ |
$2.002926308$ |
3.100989179 |
\( -\frac{327638535}{16} a + \frac{412228417}{16} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -15 a + 51\) , \( 13 a - 251\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(-15a+51\right){x}+13a-251$ |
| 36.2-a1 |
36.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
36.2 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{16} \) |
$1.68128$ |
$(3,a), (3,a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.555669112$ |
0.665439557 |
\( -\frac{7241424659}{9565938} a - \frac{44767669313}{4782969} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 3 a + 15\) , \( -9 a - 9\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(-a-1\right){x}^2+\left(3a+15\right){x}-9a-9$ |
| 36.2-a2 |
36.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
36.2 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{8} \) |
$1.68128$ |
$(3,a), (3,a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$5.111338224$ |
0.665439557 |
\( \frac{3490711}{8748} a - \frac{10786321}{8748} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 3 a + 5\) , \( -3 a + 1\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(-a-1\right){x}^2+\left(3a+5\right){x}-3a+1$ |
| 36.2-b1 |
36.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
36.2 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{16} \) |
$1.68128$ |
$(3,a), (3,a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.555669112$ |
0.665439557 |
\( \frac{7241424659}{9565938} a - \frac{32258921095}{3188646} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -3 a + 17\) , \( 6 a - 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+{x}^2+\left(-3a+17\right){x}+6a-1$ |
| 36.2-b2 |
36.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
36.2 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{8} \) |
$1.68128$ |
$(3,a), (3,a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$5.111338224$ |
0.665439557 |
\( -\frac{3490711}{8748} a - \frac{1215935}{1458} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -3 a + 7\) , \( 5\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+{x}^2+\left(-3a+7\right){x}+5$ |
| 36.3-a1 |
36.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
36.3 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{24} \) |
$1.68128$ |
$(3,a+2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$3.273009913$ |
1.704438384 |
\( \frac{423619}{5832} a - \frac{34273}{972} \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( -5 a - 17\) , \( 17 a + 54\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(-5a-17\right){x}+17a+54$ |
| 36.3-b1 |
36.3-b |
$3$ |
$9$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
36.3 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{6} \) |
$1.68128$ |
$(3,a+2), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$3.306891705$ |
$5.235122741$ |
2.003402969 |
\( \frac{81375}{2} a - 80875 \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3-a{x}^2-{x}$ |
| 36.3-b2 |
36.3-b |
$3$ |
$9$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
36.3 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{18} \) |
$1.68128$ |
$(3,a+2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$0.367432411$ |
$5.235122741$ |
2.003402969 |
\( -\frac{81375}{2} a - \frac{80375}{2} \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( 2 a - 30\) , \( 3 a + 153\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3-a{x}^2+\left(2a-30\right){x}+3a+153$ |
| 36.3-b3 |
36.3-b |
$3$ |
$9$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
36.3 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{18} \) |
$1.68128$ |
$(3,a+2), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1.102297235$ |
$5.235122741$ |
2.003402969 |
\( -\frac{42875}{8} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -5 a + 4\) , \( 14 a - 36\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3-a{x}^2+\left(-5a+4\right){x}+14a-36$ |
| 36.3-c1 |
36.3-c |
$3$ |
$9$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
36.3 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{18} \) |
$1.68128$ |
$(3,a+2), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cn, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$2.229782782$ |
$2.002926308$ |
3.100989179 |
\( \frac{2352637}{4096} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 20 a + 1\) , \( 49 a - 223\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3-a{x}^2+\left(20a+1\right){x}+49a-223$ |
| 36.3-c2 |
36.3-c |
$3$ |
$9$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
36.3 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{6} \) |
$1.68128$ |
$(3,a+2), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cn, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$6.689348348$ |
$2.002926308$ |
3.100989179 |
\( \frac{327638535}{16} a + \frac{42294941}{8} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 15 a + 36\) , \( -13 a - 238\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3-a{x}^2+\left(15a+36\right){x}-13a-238$ |
| 36.3-c3 |
36.3-c |
$3$ |
$9$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
36.3 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{18} \) |
$1.68128$ |
$(3,a+2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cn, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$0.743260927$ |
$2.002926308$ |
3.100989179 |
\( -\frac{327638535}{16} a + \frac{412228417}{16} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -128 a + 429\) , \( 305 a + 4642\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-a{x}^2+\left(-128a+429\right){x}+305a+4642$ |
| 45.1-a1 |
45.1-a |
$2$ |
$7$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{19} \cdot 5^{7} \) |
$1.77774$ |
$(3,a), (5,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$7$ |
7B |
$1$ |
\( 2 \) |
$1$ |
$2.842718108$ |
1.480361499 |
\( -\frac{34185946}{234375} a + \frac{140101531}{234375} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -7 a + 27\) , \( -21 a + 28\bigr] \) |
${y}^2+a{x}{y}={x}^3-a{x}^2+\left(-7a+27\right){x}-21a+28$ |
| 45.1-a2 |
45.1-a |
$2$ |
$7$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{13} \cdot 5 \) |
$1.77774$ |
$(3,a), (5,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$7$ |
7B |
$1$ |
\( 2 \) |
$1$ |
$2.842718108$ |
1.480361499 |
\( \frac{93129494}{10935} a + \frac{902836231}{10935} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -6 a + 7\) , \( 9 a - 9\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3-{x}^2+\left(-6a+7\right){x}+9a-9$ |
| 45.1-b1 |
45.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{23} \cdot 5^{5} \) |
$1.77774$ |
$(3,a), (5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.133271088$ |
$2.304551334$ |
3.198794293 |
\( \frac{304393331}{759375} a - \frac{8658665891}{759375} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 27 a - 32\) , \( -178 a - 209\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(27a-32\right){x}-178a-209$ |
| 45.1-b2 |
45.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{7} \cdot 5 \) |
$1.77774$ |
$(3,a), (5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B |
$1$ |
\( 2^{2} \) |
$0.666355442$ |
$2.304551334$ |
3.198794293 |
\( \frac{126562271}{15} a + \frac{2710970104}{15} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( 51\) , \( 60 a - 45\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3+\left(a-1\right){x}^2+51{x}+60a-45$ |
| 45.6-a1 |
45.6-a |
$2$ |
$7$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
45.6 |
\( 3^{2} \cdot 5 \) |
\( 3^{19} \cdot 5^{7} \) |
$1.77774$ |
$(3,a+2), (5,a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$7$ |
7B |
$1$ |
\( 2 \) |
$1$ |
$2.842718108$ |
1.480361499 |
\( \frac{34185946}{234375} a + \frac{7061039}{15625} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 7 a + 20\) , \( 21 a + 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3-{x}^2+\left(7a+20\right){x}+21a+7$ |
| 45.6-a2 |
45.6-a |
$2$ |
$7$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
45.6 |
\( 3^{2} \cdot 5 \) |
\( 3^{13} \cdot 5 \) |
$1.77774$ |
$(3,a+2), (5,a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$7$ |
7B |
$1$ |
\( 2 \) |
$1$ |
$2.842718108$ |
1.480361499 |
\( -\frac{93129494}{10935} a + \frac{66397715}{729} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( 5 a + 2\) , \( -9 a\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3-a{x}^2+\left(5a+2\right){x}-9a$ |
| 45.6-b1 |
45.6-b |
$2$ |
$5$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
45.6 |
\( 3^{2} \cdot 5 \) |
\( 3^{23} \cdot 5^{5} \) |
$1.77774$ |
$(3,a+2), (5,a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.133271088$ |
$2.304551334$ |
3.198794293 |
\( -\frac{304393331}{759375} a - \frac{556951504}{50625} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -29 a - 3\) , \( 177 a - 386\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-a{x}^2+\left(-29a-3\right){x}+177a-386$ |
| 45.6-b2 |
45.6-b |
$2$ |
$5$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
45.6 |
\( 3^{2} \cdot 5 \) |
\( 3^{7} \cdot 5 \) |
$1.77774$ |
$(3,a+2), (5,a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B |
$1$ |
\( 2^{2} \) |
$0.666355442$ |
$2.304551334$ |
3.198794293 |
\( -\frac{126562271}{15} a + 189168825 \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -a + 51\) , \( -61 a + 15\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^3-a{x}^2+\left(-a+51\right){x}-61a+15$ |
| 49.1-a1 |
49.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
49.1 |
\( 7^{2} \) |
\( 7^{6} \) |
$1.81599$ |
$(7,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 5$ |
2Cn, 5B |
$1$ |
\( 1 \) |
$1$ |
$4.811128515$ |
1.252711163 |
\( 1785 a - 671 \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( -a + 5\) , \( -3\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3+{x}^2+\left(-a+5\right){x}-3$ |
| 49.1-a2 |
49.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
49.1 |
\( 7^{2} \) |
\( 3^{12} \cdot 7^{6} \) |
$1.81599$ |
$(7,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 5$ |
2Cn, 5B |
$1$ |
\( 1 \) |
$1$ |
$4.811128515$ |
1.252711163 |
\( -1785 a + 1114 \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( -5 a - 18\) , \( -6 a - 36\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-a{x}^2+\left(-5a-18\right){x}-6a-36$ |
| 49.3-a1 |
49.3-a |
$2$ |
$5$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
49.3 |
\( 7^{2} \) |
\( 3^{12} \cdot 7^{6} \) |
$1.81599$ |
$(7,a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 5$ |
2Cn, 5B |
$1$ |
\( 1 \) |
$1$ |
$4.811128515$ |
1.252711163 |
\( 1785 a - 671 \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 5 a - 23\) , \( 6 a - 42\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(a-1\right){x}^2+\left(5a-23\right){x}+6a-42$ |
| 49.3-a2 |
49.3-a |
$2$ |
$5$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
49.3 |
\( 7^{2} \) |
\( 7^{6} \) |
$1.81599$ |
$(7,a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 5$ |
2Cn, 5B |
$1$ |
\( 1 \) |
$1$ |
$4.811128515$ |
1.252711163 |
\( -1785 a + 1114 \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( 4\) , \( -3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(-a+1\right){x}^2+4{x}-3$ |
| 57.1-a1 |
57.1-a |
$2$ |
$7$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
57.1 |
\( 3 \cdot 19 \) |
\( 3 \cdot 19 \) |
$1.88596$ |
$(3,a), (19,a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.2.3 |
$1$ |
\( 1 \) |
$0.594396850$ |
$8.265661094$ |
2.558515660 |
\( -\frac{462848}{57} a - \frac{28672}{57} \) |
\( \bigl[0\) , \( a - 1\) , \( a\) , \( -5\) , \( -a + 3\bigr] \) |
${y}^2+a{y}={x}^3+\left(a-1\right){x}^2-5{x}-a+3$ |
| 57.1-a2 |
57.1-a |
$2$ |
$7$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
57.1 |
\( 3 \cdot 19 \) |
\( 3^{7} \cdot 19^{7} \) |
$1.88596$ |
$(3,a), (19,a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.2.3 |
$1$ |
\( 1 \) |
$4.160777952$ |
$1.180808727$ |
2.558515660 |
\( \frac{507958874411008}{1954897493193} a + \frac{20053670781734912}{1954897493193} \) |
\( \bigl[0\) , \( a - 1\) , \( a\) , \( -10 a + 35\) , \( 24 a + 154\bigr] \) |
${y}^2+a{y}={x}^3+\left(a-1\right){x}^2+\left(-10a+35\right){x}+24a+154$ |
| 57.4-a1 |
57.4-a |
$2$ |
$7$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
57.4 |
\( 3 \cdot 19 \) |
\( 3 \cdot 19 \) |
$1.88596$ |
$(3,a+2), (19,a+12)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.2.1 |
$1$ |
\( 1 \) |
$0.594396850$ |
$8.265661094$ |
2.558515660 |
\( \frac{462848}{57} a - \frac{163840}{19} \) |
\( \bigl[0\) , \( -a\) , \( a + 1\) , \( -5\) , \( 2\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^3-a{x}^2-5{x}+2$ |
| 57.4-a2 |
57.4-a |
$2$ |
$7$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
57.4 |
\( 3 \cdot 19 \) |
\( 3^{7} \cdot 19^{7} \) |
$1.88596$ |
$(3,a+2), (19,a+12)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.2.1 |
$1$ |
\( 1 \) |
$4.160777952$ |
$1.180808727$ |
2.558515660 |
\( -\frac{507958874411008}{1954897493193} a + \frac{6853876552048640}{651632497731} \) |
\( \bigl[0\) , \( -a\) , \( a + 1\) , \( 10 a + 25\) , \( -25 a + 178\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^3-a{x}^2+\left(10a+25\right){x}-25a+178$ |
| 60.1-a1 |
60.1-a |
$2$ |
$7$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
60.1 |
\( 2^{2} \cdot 3 \cdot 5 \) |
\( 2^{2} \cdot 3^{26} \cdot 5^{14} \) |
$1.91030$ |
$(3,a), (5,a), (2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.2.1 |
$1$ |
\( 2^{2} \) |
$1.358278892$ |
$0.517053371$ |
2.925824678 |
\( -\frac{7007467329157740199}{58385852050781250} a + \frac{106085295545644211689}{58385852050781250} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 166 a + 1387\) , \( -3100 a - 1039\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(166a+1387\right){x}-3100a-1039$ |
| 60.1-a2 |
60.1-a |
$2$ |
$7$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
60.1 |
\( 2^{2} \cdot 3 \cdot 5 \) |
\( 2^{14} \cdot 3^{14} \cdot 5^{2} \) |
$1.91030$ |
$(3,a), (5,a), (2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.2.1 |
$1$ |
\( 2^{2} \cdot 7 \) |
$0.027719977$ |
$3.619373601$ |
2.925824678 |
\( -\frac{3212719}{28800} a + \frac{211119409}{28800} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -14 a + 37\) , \( 18 a + 107\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(-14a+37\right){x}+18a+107$ |
| 60.2-a1 |
60.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
60.2 |
\( 2^{2} \cdot 3 \cdot 5 \) |
\( 2^{2} \cdot 3^{16} \cdot 5^{2} \) |
$1.91030$ |
$(3,a), (5,a+4), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.044177495$ |
$6.427715086$ |
0.591495832 |
\( -\frac{128048}{2025} a - \frac{691507}{810} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -4 a - 11\) , \( -3 a + 39\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a+1\right){x}^2+\left(-4a-11\right){x}-3a+39$ |
| 60.3-a1 |
60.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
60.3 |
\( 2^{2} \cdot 3 \cdot 5 \) |
\( 2^{2} \cdot 3^{16} \cdot 5^{2} \) |
$1.91030$ |
$(3,a+2), (5,a), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.044177495$ |
$6.427715086$ |
0.591495832 |
\( \frac{128048}{2025} a - \frac{1237877}{1350} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( -a - 3\) , \( a + 4\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3+a{x}^2+\left(-a-3\right){x}+a+4$ |
*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.
