| 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 |
| 49.1-a1 |
49.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{10} \) |
$0.52866$ |
$(7)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B.1.4[2] |
$1$ |
\( 1 \) |
$1$ |
$1.045448192$ |
0.467538645 |
\( -\frac{2887553024}{16807} \) |
\( \bigl[0\) , \( -\phi + 1\) , \( 1\) , \( -30 \phi - 29\) , \( -102 \phi - 84\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(-30\phi-29\right){x}-102\phi-84$ |
| 1225.1-a1 |
1225.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1225.1 |
\( 5^{2} \cdot 7^{2} \) |
\( 5^{6} \cdot 7^{10} \) |
$1.18211$ |
$(-2a+1), (7)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.1.1[2] |
$1$ |
\( 2 \cdot 5 \) |
$0.664629997$ |
$6.888108064$ |
1.637890543 |
\( -\frac{2887553024}{16807} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -148\) , \( 748\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-148{x}+748$ |
| 2401.1-d1 |
2401.1-d |
$2$ |
$5$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2401.1 |
\( 7^{4} \) |
\( 7^{22} \) |
$1.39869$ |
$(7)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.1[2] |
$1$ |
\( 2 \) |
$1$ |
$2.200325409$ |
1.968030875 |
\( -\frac{2887553024}{16807} \) |
\( \bigl[0\) , \( \phi - 1\) , \( 1\) , \( -1454 \phi - 1453\) , \( 37868 \phi + 28764\bigr] \) |
${y}^2+{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(-1454\phi-1453\right){x}+37868\phi+28764$ |
| 3969.1-g1 |
3969.1-g |
$2$ |
$5$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
3969.1 |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{12} \cdot 7^{10} \) |
$1.58597$ |
$(3), (7)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$5.134092622$ |
2.296036021 |
\( -\frac{2887553024}{16807} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -267 \phi - 267\) , \( 3019 \phi + 2264\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-267\phi-267\right){x}+3019\phi+2264$ |
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*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.
