| 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-a2 |
36.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{10} \) |
$0.48944$ |
$(2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.1.4[2] |
$1$ |
\( 2 \) |
$1$ |
$1.771984867$ |
0.396227861 |
\( -\frac{19465109}{248832} \) |
\( \bigl[\phi + 1\) , \( \phi\) , \( \phi\) , \( -5 \phi - 5\) , \( -51 \phi - 37\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\phi{x}^{2}+\left(-5\phi-5\right){x}-51\phi-37$ |
| 324.1-a2 |
324.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{20} \cdot 3^{22} \) |
$0.84773$ |
$(2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$2.333171679$ |
1.043426095 |
\( -\frac{19465109}{248832} \) |
\( \bigl[\phi\) , \( -\phi - 1\) , \( \phi + 1\) , \( 50 \phi - 101\) , \( -1186 \phi + 2086\bigr] \) |
${y}^2+\phi{x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(50\phi-101\right){x}-1186\phi+2086$ |
| 900.1-a2 |
900.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{10} \cdot 5^{6} \) |
$1.09442$ |
$(-2a+1), (2), (3)$ |
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 |
\( -\frac{19465109}{248832} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -28\) , \( 272\bigr] \) |
${y}^2+{x}{y}={x}^{3}-28{x}+272$ |
| 2304.1-i2 |
2304.1-i |
$4$ |
$10$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{44} \cdot 3^{10} \) |
$1.38434$ |
$(2), (3)$ |
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 |
\( -\frac{19465109}{248832} \) |
\( \bigl[0\) , \( -\phi - 1\) , \( 0\) , \( \phi - 89\) , \( -1375 \phi + 732\bigr] \) |
${y}^2={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(\phi-89\right){x}-1375\phi+732$ |
| 2304.1-l2 |
2304.1-l |
$4$ |
$10$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{44} \cdot 3^{10} \) |
$1.38434$ |
$(2), (3)$ |
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 |
\( -\frac{19465109}{248832} \) |
\( \bigl[0\) , \( \phi + 1\) , \( 0\) , \( \phi - 89\) , \( 1375 \phi - 732\bigr] \) |
${y}^2={x}^{3}+\left(\phi+1\right){x}^{2}+\left(\phi-89\right){x}+1375\phi-732$ |
| 2304.1-q2 |
2304.1-q |
$4$ |
$10$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{44} \cdot 3^{10} \) |
$1.38434$ |
$(2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$1.749878759$ |
0.782569571 |
\( -\frac{19465109}{248832} \) |
\( \bigl[0\) , \( \phi\) , \( 0\) , \( 90 \phi - 179\) , \( -2839 \phi + 4946\bigr] \) |
${y}^2={x}^{3}+\phi{x}^{2}+\left(90\phi-179\right){x}-2839\phi+4946$ |
| 4356.2-l2 |
4356.2-l |
$4$ |
$10$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4356.2 |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{20} \cdot 3^{10} \cdot 11^{6} \) |
$1.62329$ |
$(-3a+2), (2), (3)$ |
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 |
\( -\frac{19465109}{248832} \) |
\( \bigl[\phi\) , \( 1\) , \( \phi + 1\) , \( -40 \phi - 56\) , \( -1254 \phi - 455\bigr] \) |
${y}^2+\phi{x}{y}+\left(\phi+1\right){y}={x}^{3}+{x}^{2}+\left(-40\phi-56\right){x}-1254\phi-455$ |
| 4356.3-l2 |
4356.3-l |
$4$ |
$10$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4356.3 |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{20} \cdot 3^{10} \cdot 11^{6} \) |
$1.62329$ |
$(-3a+1), (2), (3)$ |
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 |
\( -\frac{19465109}{248832} \) |
\( \bigl[\phi + 1\) , \( -\phi + 1\) , \( \phi\) , \( 38 \phi - 95\) , \( 1253 \phi - 1708\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(38\phi-95\right){x}+1253\phi-1708$ |
*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.
