| 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 |
| 1024.1-b4 |
1024.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( - 2^{18} \) |
$1.13031$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$13.36728142$ |
1.494507497 |
\( 14540840 a + 8987328 \) |
\( \bigl[0\) , \( -\phi + 1\) , \( 0\) , \( -10 \phi - 1\) , \( 15 \phi + 7\bigr] \) |
${y}^2={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(-10\phi-1\right){x}+15\phi+7$ |
| 1024.1-d4 |
1024.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( - 2^{18} \) |
$1.13031$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4.855651403$ |
1.085756661 |
\( 14540840 a + 8987328 \) |
\( \bigl[0\) , \( -\phi - 1\) , \( 0\) , \( -7 \phi + 7\) , \( 9 \phi - 16\bigr] \) |
${y}^2={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-7\phi+7\right){x}+9\phi-16$ |
| 1024.1-g4 |
1024.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( - 2^{18} \) |
$1.13031$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$6.313756918$ |
1.411798966 |
\( 14540840 a + 8987328 \) |
\( \bigl[0\) , \( \phi - 1\) , \( 0\) , \( -10 \phi - 1\) , \( -15 \phi - 7\bigr] \) |
${y}^2={x}^{3}+\left(\phi-1\right){x}^{2}+\left(-10\phi-1\right){x}-15\phi-7$ |
| 1024.1-i4 |
1024.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( - 2^{18} \) |
$1.13031$ |
$(2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.758915454$ |
$17.38134775$ |
1.474795663 |
\( 14540840 a + 8987328 \) |
\( \bigl[0\) , \( \phi + 1\) , \( 0\) , \( -7 \phi + 7\) , \( -9 \phi + 16\bigr] \) |
${y}^2={x}^{3}+\left(\phi+1\right){x}^{2}+\left(-7\phi+7\right){x}-9\phi+16$ |
| 4096.1-h4 |
4096.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( - 2^{30} \) |
$1.59850$ |
$(2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$2.436102655$ |
$2.427825701$ |
2.645014686 |
\( 14540840 a + 8987328 \) |
\( \bigl[0\) , \( \phi + 1\) , \( 0\) , \( -31 \phi + 26\) , \( 36 \phi - 133\bigr] \) |
${y}^2={x}^{3}+\left(\phi+1\right){x}^{2}+\left(-31\phi+26\right){x}+36\phi-133$ |
| 4096.1-o4 |
4096.1-o |
$4$ |
$4$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( - 2^{30} \) |
$1.59850$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$8.690673875$ |
1.943293755 |
\( 14540840 a + 8987328 \) |
\( \bigl[0\) , \( -\phi - 1\) , \( 0\) , \( -31 \phi + 26\) , \( -36 \phi + 133\bigr] \) |
${y}^2={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-31\phi+26\right){x}-36\phi+133$ |
| 4096.1-t4 |
4096.1-t |
$4$ |
$4$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( - 2^{30} \) |
$1.59850$ |
$(2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.530312453$ |
$6.683640713$ |
2.287063434 |
\( 14540840 a + 8987328 \) |
\( \bigl[0\) , \( \phi - 1\) , \( 0\) , \( -39 \phi - 6\) , \( 114 \phi + 23\bigr] \) |
${y}^2={x}^{3}+\left(\phi-1\right){x}^{2}+\left(-39\phi-6\right){x}+114\phi+23$ |
| 4096.1-z4 |
4096.1-z |
$4$ |
$4$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( - 2^{30} \) |
$1.59850$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.156878459$ |
1.411798966 |
\( 14540840 a + 8987328 \) |
\( \bigl[0\) , \( -\phi + 1\) , \( 0\) , \( -39 \phi - 6\) , \( -114 \phi - 23\bigr] \) |
${y}^2={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(-39\phi-6\right){x}-114\phi-23$ |
*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.
