| 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 |
| 36.1-a3 |
36.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{20} \) |
$0.48944$ |
$(2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.1.4[2] |
$1$ |
\( 2 \) |
$1$ |
$1.771984867$ |
0.396227861 |
\( \frac{502270291349}{1889568} \) |
\( \bigl[\phi\) , \( \phi - 1\) , \( \phi\) , \( 165 \phi - 331\) , \( 1352 \phi - 2408\bigr] \) |
${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(165\phi-331\right){x}+1352\phi-2408$ |
| 324.1-a3 |
324.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{10} \cdot 3^{32} \) |
$0.84773$ |
$(2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$2.333171679$ |
1.043426095 |
\( \frac{502270291349}{1889568} \) |
\( \bigl[\phi + 1\) , \( 1\) , \( 1\) , \( -1490 \phi - 1490\) , \( 37999 \phi + 28499\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-1490\phi-1490\right){x}+37999\phi+28499$ |
| 900.1-a3 |
900.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{20} \cdot 5^{6} \) |
$1.09442$ |
$(-2a+1), (2), (3)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 5$ |
2B, 5B.1.1[2] |
$1$ |
\( 2^{2} \cdot 5^{2} \) |
$1$ |
$3.130278287$ |
1.399903007 |
\( \frac{502270291349}{1889568} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -828\) , \( 9072\bigr] \) |
${y}^2+{x}{y}={x}^{3}-828{x}+9072$ |
| 2304.1-i3 |
2304.1-i |
$4$ |
$10$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{34} \cdot 3^{20} \) |
$1.38434$ |
$(2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$0.880448562$ |
1.968742835 |
\( \frac{502270291349}{1889568} \) |
\( \bigl[0\) , \( -\phi - 1\) , \( 0\) , \( \phi - 2649\) , \( -45919 \phi + 24284\bigr] \) |
${y}^2={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(\phi-2649\right){x}-45919\phi+24284$ |
| 2304.1-l3 |
2304.1-l |
$4$ |
$10$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{34} \cdot 3^{20} \) |
$1.38434$ |
$(2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$0.880448562$ |
1.968742835 |
\( \frac{502270291349}{1889568} \) |
\( \bigl[0\) , \( \phi + 1\) , \( 0\) , \( \phi - 2649\) , \( 45919 \phi - 24284\bigr] \) |
${y}^2={x}^{3}+\left(\phi+1\right){x}^{2}+\left(\phi-2649\right){x}+45919\phi-24284$ |
| 2304.1-q3 |
2304.1-q |
$4$ |
$10$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{34} \cdot 3^{20} \) |
$1.38434$ |
$(2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$1.749878759$ |
0.782569571 |
\( \frac{502270291349}{1889568} \) |
\( \bigl[0\) , \( \phi\) , \( 0\) , \( 2650 \phi - 5299\) , \( -94487 \phi + 164690\bigr] \) |
${y}^2={x}^{3}+\phi{x}^{2}+\left(2650\phi-5299\right){x}-94487\phi+164690$ |
| 4356.2-l3 |
4356.2-l |
$4$ |
$10$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4356.2 |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{10} \cdot 3^{20} \cdot 11^{6} \) |
$1.62329$ |
$(-3a+2), (2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$1.061860919$ |
2.374393198 |
\( \frac{502270291349}{1889568} \) |
\( \bigl[\phi\) , \( 1\) , \( \phi + 1\) , \( -1160 \phi - 1656\) , \( -41670 \phi - 15047\bigr] \) |
${y}^2+\phi{x}{y}+\left(\phi+1\right){y}={x}^{3}+{x}^{2}+\left(-1160\phi-1656\right){x}-41670\phi-15047$ |
| 4356.3-l3 |
4356.3-l |
$4$ |
$10$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4356.3 |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{10} \cdot 3^{20} \cdot 11^{6} \) |
$1.62329$ |
$(-3a+1), (2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$1.061860919$ |
2.374393198 |
\( \frac{502270291349}{1889568} \) |
\( \bigl[\phi + 1\) , \( -\phi + 1\) , \( \phi\) , \( 1158 \phi - 2815\) , \( 41669 \phi - 56716\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(1158\phi-2815\right){x}+41669\phi-56716$ |
*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.
