| 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 |
| 1444.1-a1 |
1444.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1444.1 |
\( 2^{2} \cdot 19^{2} \) |
\( 2^{2} \cdot 19^{4} \) |
$1.23173$ |
$(4a-3), (-4a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.037876241$ |
$15.44068294$ |
1.569277078 |
\( \frac{336865267}{13718} a - \frac{521369813}{13718} \) |
\( \bigl[\phi + 1\) , \( \phi - 1\) , \( 0\) , \( 4 \phi - 1\) , \( -\phi + 5\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(4\phi-1\right){x}-\phi+5$ |
| 1444.1-b1 |
1444.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1444.1 |
\( 2^{2} \cdot 19^{2} \) |
\( 2^{6} \cdot 19^{2} \) |
$1.23173$ |
$(4a-3), (-4a+1), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$0.188760387$ |
$32.17041206$ |
1.810469536 |
\( -\frac{413493625}{152} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -16\) , \( 22\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-16{x}+22$ |
| 1444.1-b2 |
1444.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1444.1 |
\( 2^{2} \cdot 19^{2} \) |
\( 2^{54} \cdot 19^{2} \) |
$1.23173$ |
$(4a-3), (-4a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 3^{3} \) |
$0.188760387$ |
$0.397165580$ |
1.810469536 |
\( -\frac{69173457625}{2550136832} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -86\) , \( -2456\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-86{x}-2456$ |
| 1444.1-b3 |
1444.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1444.1 |
\( 2^{2} \cdot 19^{2} \) |
\( 2^{18} \cdot 19^{6} \) |
$1.23173$ |
$(4a-3), (-4a+1), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3^{4} \) |
$0.062920129$ |
$3.574490228$ |
1.810469536 |
\( \frac{94196375}{3511808} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 9\) , \( 90\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+9{x}+90$ |
| 1444.1-c1 |
1444.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1444.1 |
\( 2^{2} \cdot 19^{2} \) |
\( 2^{2} \cdot 19^{4} \) |
$1.23173$ |
$(4a-3), (-4a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.037876241$ |
$15.44068294$ |
1.569277078 |
\( -\frac{336865267}{13718} a - \frac{92252273}{6859} \) |
\( \bigl[\phi\) , \( \phi + 1\) , \( \phi + 1\) , \( -3 \phi + 2\) , \( -\phi\bigr] \) |
${y}^2+\phi{x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(\phi+1\right){x}^{2}+\left(-3\phi+2\right){x}-\phi$ |
| 1444.1-d1 |
1444.1-d |
$2$ |
$5$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1444.1 |
\( 2^{2} \cdot 19^{2} \) |
\( 2^{2} \cdot 19^{10} \) |
$1.23173$ |
$(4a-3), (-4a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.4[2] |
$1$ |
\( 1 \) |
$2.731722053$ |
$0.671163407$ |
1.639871327 |
\( -\frac{37966934881}{4952198} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -70\) , \( -279\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-70{x}-279$ |
| 1444.1-d2 |
1444.1-d |
$2$ |
$5$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1444.1 |
\( 2^{2} \cdot 19^{2} \) |
\( 2^{10} \cdot 19^{2} \) |
$1.23173$ |
$(4a-3), (-4a+1), (2)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1[2] |
$1$ |
\( 5 \) |
$0.546344410$ |
$16.77908518$ |
1.639871327 |
\( -\frac{1}{608} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+1$ |
*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.
