| 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 |
| 18.1-a1 |
18.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{11} \) |
$1.55091$ |
$(2,a), (3,a)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B |
$1$ |
\( 2^{3} \) |
$0.027600400$ |
$4.130840138$ |
0.865973438 |
\( -\frac{1622401}{972} a - \frac{232949}{972} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( -a + 18\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^3+\left(-a-1\right){x}^2+\left(-a+18\right){x}$ |
| 18.1-a2 |
18.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{7} \cdot 5^{12} \) |
$1.55091$ |
$(2,a), (3,a)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B |
$1$ |
\( 2^{3} \) |
$0.027600400$ |
$4.130840138$ |
0.865973438 |
\( -\frac{68401}{3072} a + \frac{91291}{3072} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 2 a - 9\) , \( 51 a - 27\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^3+\left(-a-1\right){x}^2+\left(2a-9\right){x}+51a-27$ |
| 18.6-a1 |
18.6-a |
$2$ |
$5$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
18.6 |
\( 2 \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{11} \) |
$1.55091$ |
$(2,a+1), (3,a+2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B |
$1$ |
\( 2^{3} \) |
$0.027600400$ |
$4.130840138$ |
0.865973438 |
\( \frac{1622401}{972} a - \frac{103075}{54} \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -a + 18\) , \( -a\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(-a+18\right){x}-a$ |
| 18.6-a2 |
18.6-a |
$2$ |
$5$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
18.6 |
\( 2 \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{7} \cdot 5^{12} \) |
$1.55091$ |
$(2,a+1), (3,a+2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B |
$1$ |
\( 2^{3} \) |
$0.027600400$ |
$4.130840138$ |
0.865973438 |
\( \frac{68401}{3072} a + \frac{3815}{512} \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -4 a - 6\) , \( -52 a + 24\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(-4a-6\right){x}-52a+24$ |
| 20.3-a1 |
20.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
20.3 |
\( 2^{2} \cdot 5 \) |
\( 2^{12} \cdot 5^{16} \) |
$1.59230$ |
$(2,a), (2,a+1), (5,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 5 \cdot 7 \) |
$0.024482576$ |
$4.051410860$ |
3.296038444 |
\( \frac{3606977}{80000} a + \frac{49778001}{80000} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -13 a + 12\) , \( -32 a - 27\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^3+\left(a-1\right){x}^2+\left(-13a+12\right){x}-32a-27$ |
| 20.4-a1 |
20.4-a |
$1$ |
$1$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
20.4 |
\( 2^{2} \cdot 5 \) |
\( 2^{12} \cdot 5^{16} \) |
$1.59230$ |
$(2,a), (2,a+1), (5,a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 5 \cdot 7 \) |
$0.024482576$ |
$4.051410860$ |
3.296038444 |
\( -\frac{3606977}{80000} a + \frac{26692489}{40000} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( 12 a\) , \( 31 a - 58\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3-a{x}^2+12a{x}+31a-58$ |
| 24.1-a1 |
24.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{10} \cdot 3^{23} \) |
$1.66656$ |
$(2,a), (3,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$2.440355859$ |
1.158467829 |
\( -\frac{586401988}{177147} a + \frac{3206166124}{177147} \) |
\( \bigl[0\) , \( a - 1\) , \( a\) , \( 21 a - 102\) , \( 83 a - 315\bigr] \) |
${y}^2+a{y}={x}^3+\left(a-1\right){x}^2+\left(21a-102\right){x}+83a-315$ |
| 24.1-b1 |
24.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{23} \cdot 3^{4} \) |
$1.66656$ |
$(2,a), (3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.210919813$ |
0.381066074 |
\( -\frac{3309649}{81} a - \frac{72125696}{81} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -6 a - 44\) , \( -17 a - 42\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2+\left(-6a-44\right){x}-17a-42$ |
| 24.1-b2 |
24.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{8} \cdot 3 \cdot 5^{12} \) |
$1.66656$ |
$(2,a), (3,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.421839627$ |
0.381066074 |
\( -\frac{18083}{3} a - \frac{124270}{3} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 12 a + 25\) , \( -12 a + 114\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2+\left(12a+25\right){x}-12a+114$ |
| 24.1-b3 |
24.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{22} \cdot 3^{2} \) |
$1.66656$ |
$(2,a), (3,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.421839627$ |
0.381066074 |
\( \frac{1625}{9} a + \frac{4702}{9} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -a + 6\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2+\left(-a+6\right){x}$ |
| 24.1-b4 |
24.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{11} \cdot 3 \) |
$1.66656$ |
$(2,a), (3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$6.421839627$ |
0.381066074 |
\( -\frac{1555}{3} a + \frac{7828}{3} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -a + 11\) , \( a - 8\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2+\left(-a+11\right){x}+a-8$ |
| 24.8-a1 |
24.8-a |
$1$ |
$1$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
24.8 |
\( 2^{3} \cdot 3 \) |
\( 2^{10} \cdot 3^{23} \) |
$1.66656$ |
$(2,a+1), (3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$2.440355859$ |
1.158467829 |
\( \frac{586401988}{177147} a + \frac{291084904}{19683} \) |
\( \bigl[0\) , \( -a\) , \( a + 1\) , \( -21 a - 81\) , \( -84 a - 232\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^3-a{x}^2+\left(-21a-81\right){x}-84a-232$ |
| 24.8-b1 |
24.8-b |
$4$ |
$4$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
24.8 |
\( 2^{3} \cdot 3 \) |
\( 2^{23} \cdot 3^{4} \) |
$1.66656$ |
$(2,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.210919813$ |
0.381066074 |
\( \frac{3309649}{81} a - \frac{8381705}{9} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 6 a - 50\) , \( 17 a - 59\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(-a-1\right){x}^2+\left(6a-50\right){x}+17a-59$ |
| 24.8-b2 |
24.8-b |
$4$ |
$4$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
24.8 |
\( 2^{3} \cdot 3 \) |
\( 2^{8} \cdot 3 \cdot 5^{12} \) |
$1.66656$ |
$(2,a+1), (3,a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.421839627$ |
0.381066074 |
\( \frac{18083}{3} a - 47451 \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -12 a + 37\) , \( 12 a + 102\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(-a-1\right){x}^2+\left(-12a+37\right){x}+12a+102$ |
| 24.8-b3 |
24.8-b |
$4$ |
$4$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
24.8 |
\( 2^{3} \cdot 3 \) |
\( 2^{22} \cdot 3^{2} \) |
$1.66656$ |
$(2,a+1), (3,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.421839627$ |
0.381066074 |
\( -\frac{1625}{9} a + 703 \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( a + 5\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(-a-1\right){x}^2+\left(a+5\right){x}$ |
| 24.8-b4 |
24.8-b |
$4$ |
$4$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
24.8 |
\( 2^{3} \cdot 3 \) |
\( 2^{11} \cdot 3 \) |
$1.66656$ |
$(2,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$6.421839627$ |
0.381066074 |
\( \frac{1555}{3} a + 2091 \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( a + 10\) , \( -a - 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(-a-1\right){x}^2+\left(a+10\right){x}-a-7$ |
| 30.1-a1 |
30.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
30.1 |
\( 2 \cdot 3 \cdot 5 \) |
\( 2^{8} \cdot 3^{17} \cdot 5^{2} \) |
$1.76217$ |
$(2,a), (3,a), (5,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{4} \) |
$0.067285044$ |
$4.079522446$ |
2.084868522 |
\( -\frac{692117353}{1555200} a - \frac{695412989}{1555200} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 3 a - 2\) , \( -19 a - 53\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3-{x}^2+\left(3a-2\right){x}-19a-53$ |
| 30.8-a1 |
30.8-a |
$1$ |
$1$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
30.8 |
\( 2 \cdot 3 \cdot 5 \) |
\( 2^{8} \cdot 3^{17} \cdot 5^{2} \) |
$1.76217$ |
$(2,a+1), (3,a+2), (5,a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{4} \) |
$0.067285044$ |
$4.079522446$ |
2.084868522 |
\( \frac{692117353}{1555200} a - \frac{77085019}{86400} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -4 a + 2\) , \( 19 a - 72\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3-a{x}^2+\left(-4a+2\right){x}+19a-72$ |
| 32.2-a1 |
32.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
32.2 |
\( 2^{5} \) |
\( 2^{14} \cdot 3^{12} \) |
$1.79083$ |
$(2,a), (2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.099324792$ |
$6.104981960$ |
0.575708795 |
\( -\frac{1285}{8} a - \frac{801}{4} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( 4 a + 8\) , \( -8 a + 16\bigr] \) |
${y}^2+a{x}{y}={x}^3-a{x}^2+\left(4a+8\right){x}-8a+16$ |
| 32.2-b1 |
32.2-b |
$3$ |
$25$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
32.2 |
\( 2^{5} \) |
\( 2^{38} \cdot 3^{12} \) |
$1.79083$ |
$(2,a), (2,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.511200951$ |
1.434772457 |
\( \frac{10456234965}{33554432} a + \frac{34842889817}{33554432} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 7 a + 177\) , \( 189 a - 997\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+\left(a+1\right){x}^2+\left(7a+177\right){x}+189a-997$ |
| 32.2-b2 |
32.2-b |
$3$ |
$25$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
32.2 |
\( 2^{5} \) |
\( 2^{50} \) |
$1.79083$ |
$(2,a), (2,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.511200951$ |
1.434772457 |
\( -\frac{10456234965}{33554432} a + \frac{22649562391}{16777216} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -14 a - 48\) , \( 44 a + 272\bigr] \) |
${y}^2+a{x}{y}={x}^3+{x}^2+\left(-14a-48\right){x}+44a+272$ |
| 32.2-b3 |
32.2-b |
$3$ |
$25$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
32.2 |
\( 2^{5} \) |
\( 2^{34} \) |
$1.79083$ |
$(2,a), (2,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.511200951$ |
1.434772457 |
\( \frac{3131359847}{32} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 482\) , \( 1146 a - 332\bigr] \) |
${y}^2={x}^3+\left(a+1\right){x}^2+\left(a+482\right){x}+1146a-332$ |
| 32.2-c1 |
32.2-c |
$3$ |
$9$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
32.2 |
\( 2^{5} \) |
\( 2^{22} \cdot 3^{12} \) |
$1.79083$ |
$(2,a), (2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1.098156126$ |
$3.735131983$ |
3.894312995 |
\( \frac{292125}{512} a - \frac{349375}{512} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -5 a - 18\) , \( -13 a + 18\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(-5a-18\right){x}-13a+18$ |
| 32.2-c2 |
32.2-c |
$3$ |
$9$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
32.2 |
\( 2^{5} \) |
\( 2^{22} \cdot 5^{12} \) |
$1.79083$ |
$(2,a), (2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.122017347$ |
$3.735131983$ |
3.894312995 |
\( -\frac{292125}{512} a - \frac{28625}{256} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -25 a + 23\) , \( 108 a - 148\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(a-1\right){x}^2+\left(-25a+23\right){x}+108a-148$ |
| 32.2-c3 |
32.2-c |
$3$ |
$9$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
32.2 |
\( 2^{5} \) |
\( 2^{30} \) |
$1.79083$ |
$(2,a), (2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$0.366052042$ |
$3.735131983$ |
3.894312995 |
\( \frac{857375}{8} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 26\) , \( 6 a - 16\bigr] \) |
${y}^2={x}^3+\left(-a-1\right){x}^2+\left(a+26\right){x}+6a-16$ |
| 32.5-a1 |
32.5-a |
$1$ |
$1$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
32.5 |
\( 2^{5} \) |
\( 2^{14} \cdot 3^{12} \) |
$1.79083$ |
$(2,a), (2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.099324792$ |
$6.104981960$ |
0.575708795 |
\( \frac{1285}{8} a - \frac{2887}{8} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -4 a + 12\) , \( 8 a + 8\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3-{x}^2+\left(-4a+12\right){x}+8a+8$ |
| 32.5-b1 |
32.5-b |
$3$ |
$25$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
32.5 |
\( 2^{5} \) |
\( 2^{50} \) |
$1.79083$ |
$(2,a), (2,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.511200951$ |
1.434772457 |
\( \frac{10456234965}{33554432} a + \frac{34842889817}{33554432} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 14 a - 62\) , \( -44 a + 316\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(-a+1\right){x}^2+\left(14a-62\right){x}-44a+316$ |
| 32.5-b2 |
32.5-b |
$3$ |
$25$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
32.5 |
\( 2^{5} \) |
\( 2^{38} \cdot 3^{12} \) |
$1.79083$ |
$(2,a), (2,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.511200951$ |
1.434772457 |
\( -\frac{10456234965}{33554432} a + \frac{22649562391}{16777216} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -15 a + 174\) , \( -6 a - 802\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a-1\right){x}^2+\left(-15a+174\right){x}-6a-802$ |
| 32.5-b3 |
32.5-b |
$3$ |
$25$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
32.5 |
\( 2^{5} \) |
\( 2^{34} \) |
$1.79083$ |
$(2,a), (2,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.511200951$ |
1.434772457 |
\( \frac{3131359847}{32} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 482\) , \( -1146 a + 332\bigr] \) |
${y}^2={x}^3+\left(-a-1\right){x}^2+\left(a+482\right){x}-1146a+332$ |
| 32.5-c1 |
32.5-c |
$3$ |
$9$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
32.5 |
\( 2^{5} \) |
\( 2^{22} \cdot 5^{12} \) |
$1.79083$ |
$(2,a), (2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.122017347$ |
$3.735131983$ |
3.894312995 |
\( \frac{292125}{512} a - \frac{349375}{512} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 17 a - 11\) , \( -85 a - 409\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+a{x}^2+\left(17a-11\right){x}-85a-409$ |
| 32.5-c2 |
32.5-c |
$3$ |
$9$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
32.5 |
\( 2^{5} \) |
\( 2^{22} \cdot 3^{12} \) |
$1.79083$ |
$(2,a), (2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1.098156126$ |
$3.735131983$ |
3.894312995 |
\( -\frac{292125}{512} a - \frac{28625}{256} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 5 a - 23\) , \( 13 a + 5\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3-a{x}^2+\left(5a-23\right){x}+13a+5$ |
| 32.5-c3 |
32.5-c |
$3$ |
$9$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
32.5 |
\( 2^{5} \) |
\( 2^{30} \) |
$1.79083$ |
$(2,a), (2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$0.366052042$ |
$3.735131983$ |
3.894312995 |
\( \frac{857375}{8} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 26\) , \( -6 a + 16\bigr] \) |
${y}^2={x}^3+\left(a+1\right){x}^2+\left(a+26\right){x}-6a+16$ |
| 36.1-a1 |
36.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{19} \) |
$1.84435$ |
$(2,a), (3,a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1.375474280$ |
$3.793552811$ |
3.302692666 |
\( -\frac{19408}{3} a - \frac{67088}{3} \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 3 a - 57\) , \( -14 a + 169\bigr] \) |
${y}^2+a{y}={x}^3+\left(3a-57\right){x}-14a+169$ |
| 36.1-a2 |
36.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{9} \) |
$1.84435$ |
$(2,a), (3,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \) |
$0.458491426$ |
$3.793552811$ |
3.302692666 |
\( -\frac{2512}{27} a + \frac{41968}{27} \) |
\( \bigl[0\) , \( a\) , \( a\) , \( -3\) , \( 7\bigr] \) |
${y}^2+a{y}={x}^3+a{x}^2-3{x}+7$ |
| 36.4-a1 |
36.4-a |
$3$ |
$25$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
36.4 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{26} \cdot 3^{6} \) |
$1.84435$ |
$(2,a), (2,a+1), (3,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 1 \) |
$3.212425095$ |
$1.744984552$ |
2.661064575 |
\( \frac{10456234965}{33554432} a + \frac{34842889817}{33554432} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 4 a\) , \( -6 a + 4\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(-a-1\right){x}^2+4a{x}-6a+4$ |
| 36.4-a2 |
36.4-a |
$3$ |
$25$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
36.4 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{26} \cdot 3^{18} \) |
$1.84435$ |
$(2,a), (2,a+1), (3,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 5^{2} \) |
$0.128497003$ |
$1.744984552$ |
2.661064575 |
\( -\frac{10456234965}{33554432} a + \frac{22649562391}{16777216} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -29 a + 81\) , \( -66 a + 481\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3-{x}^2+\left(-29a+81\right){x}-66a+481$ |
| 36.4-a3 |
36.4-a |
$3$ |
$25$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
36.4 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{6} \cdot 5^{12} \) |
$1.84435$ |
$(2,a), (2,a+1), (3,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 5 \) |
$0.642485019$ |
$1.744984552$ |
2.661064575 |
\( \frac{3131359847}{32} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -243 a - 1926\) , \( -5643 a - 29966\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(-a-1\right){x}^2+\left(-243a-1926\right){x}-5643a-29966$ |
| 36.4-b1 |
36.4-b |
$2$ |
$2$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
36.4 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{13} \cdot 3^{15} \) |
$1.84435$ |
$(2,a), (2,a+1), (3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$4.546039831$ |
4.316125351 |
\( \frac{136781}{256} a - \frac{858483}{128} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 3 a - 33\) , \( 15 a - 37\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(-a-1\right){x}^2+\left(3a-33\right){x}+15a-37$ |
| 36.4-b2 |
36.4-b |
$2$ |
$2$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
36.4 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{15} \) |
$1.84435$ |
$(2,a), (2,a+1), (3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$4.546039831$ |
4.316125351 |
\( \frac{86075}{1024} a - \frac{1594953}{1024} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -5 a + 3\) , \( -6 a + 43\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3-{x}^2+\left(-5a+3\right){x}-6a+43$ |
| 36.4-c1 |
36.4-c |
$3$ |
$9$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
36.4 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{6} \) |
$1.84435$ |
$(2,a), (2,a+1), (3,a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1.750768396$ |
$4.312958912$ |
3.584551597 |
\( \frac{292125}{512} a - \frac{349375}{512} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -9 a + 4\) , \( 5 a + 29\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a-1\right){x}^2+\left(-9a+4\right){x}+5a+29$ |
| 36.4-c2 |
36.4-c |
$3$ |
$9$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
36.4 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{6} \cdot 5^{12} \) |
$1.84435$ |
$(2,a), (2,a+1), (3,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1.750768396$ |
$4.312958912$ |
3.584551597 |
\( -\frac{292125}{512} a - \frac{28625}{256} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -16 a + 4\) , \( -47 a + 245\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(a-1\right){x}^2+\left(-16a+4\right){x}-47a+245$ |
| 36.4-c3 |
36.4-c |
$3$ |
$9$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
36.4 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{6} \cdot 5^{12} \) |
$1.84435$ |
$(2,a), (2,a+1), (3,a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$5.252305188$ |
$4.312958912$ |
3.584551597 |
\( \frac{857375}{8} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -16 a - 131\) , \( -149 a - 349\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(a-1\right){x}^2+\left(-16a-131\right){x}-149a-349$ |
| 36.6-a1 |
36.6-a |
$3$ |
$9$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
36.6 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{6} \cdot 5^{12} \) |
$1.84435$ |
$(2,a), (2,a+1), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1.750768396$ |
$4.312958912$ |
3.584551597 |
\( \frac{292125}{512} a - \frac{349375}{512} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 16 a - 12\) , \( 47 a + 198\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-a{x}^2+\left(16a-12\right){x}+47a+198$ |
| 36.6-a2 |
36.6-a |
$3$ |
$9$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
36.6 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{6} \) |
$1.84435$ |
$(2,a), (2,a+1), (3,a+2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1.750768396$ |
$4.312958912$ |
3.584551597 |
\( -\frac{292125}{512} a - \frac{28625}{256} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -3\) , \( -a - 28\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(a+1\right){x}^2-3{x}-a-28$ |
| 36.6-a3 |
36.6-a |
$3$ |
$9$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
36.6 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{6} \cdot 5^{12} \) |
$1.84435$ |
$(2,a), (2,a+1), (3,a+2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$5.252305188$ |
$4.312958912$ |
3.584551597 |
\( \frac{857375}{8} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 16 a - 147\) , \( 149 a - 498\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-a{x}^2+\left(16a-147\right){x}+149a-498$ |
| 36.6-b1 |
36.6-b |
$3$ |
$25$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
36.6 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{26} \cdot 3^{18} \) |
$1.84435$ |
$(2,a), (2,a+1), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 5^{2} \) |
$0.128497003$ |
$1.744984552$ |
2.661064575 |
\( \frac{10456234965}{33554432} a + \frac{34842889817}{33554432} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 28 a + 52\) , \( 65 a + 415\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(28a+52\right){x}+65a+415$ |
| 36.6-b2 |
36.6-b |
$3$ |
$25$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
36.6 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{26} \cdot 3^{6} \) |
$1.84435$ |
$(2,a), (2,a+1), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 1 \) |
$3.212425095$ |
$1.744984552$ |
2.661064575 |
\( -\frac{10456234965}{33554432} a + \frac{22649562391}{16777216} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -2 a + 3\) , \( 3 a + 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(a+1\right){x}^2+\left(-2a+3\right){x}+3a+1$ |
| 36.6-b3 |
36.6-b |
$3$ |
$25$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
36.6 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{6} \cdot 5^{12} \) |
$1.84435$ |
$(2,a), (2,a+1), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 5 \) |
$0.642485019$ |
$1.744984552$ |
2.661064575 |
\( \frac{3131359847}{32} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 245 a - 2170\) , \( 5887 a - 37779\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(a+1\right){x}^2+\left(245a-2170\right){x}+5887a-37779$ |
| 36.6-c1 |
36.6-c |
$2$ |
$2$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
36.6 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{13} \cdot 3^{15} \) |
$1.84435$ |
$(2,a), (2,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$4.546039831$ |
4.316125351 |
\( -\frac{136781}{256} a - \frac{1580185}{256} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -a - 31\) , \( -17 a - 53\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(a+1\right){x}^2+\left(-a-31\right){x}-17a-53$ |
| 36.6-c2 |
36.6-c |
$2$ |
$2$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
36.6 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{15} \) |
$1.84435$ |
$(2,a), (2,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$4.546039831$ |
4.316125351 |
\( -\frac{86075}{1024} a - \frac{754439}{512} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 4 a - 2\) , \( 5 a + 37\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(4a-2\right){x}+5a+37$ |
*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.
