| 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-a1 |
36.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{2} \) |
$0.48944$ |
$(2), (3)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.1.1[2] |
$1$ |
\( 2 \) |
$1$ |
$44.29962169$ |
0.396227861 |
\( -\frac{24389}{12} \) |
\( \bigl[\phi + 1\) , \( \phi\) , \( \phi\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\phi{x}^{2}$ |
| 324.1-a1 |
324.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{4} \cdot 3^{14} \) |
$0.84773$ |
$(2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$2.333171679$ |
1.043426095 |
\( -\frac{24389}{12} \) |
\( \bigl[\phi + 1\) , \( 1\) , \( 1\) , \( -5 \phi - 5\) , \( -17 \phi - 13\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-5\phi-5\right){x}-17\phi-13$ |
| 900.1-a1 |
900.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 5^{6} \) |
$1.09442$ |
$(-2a+1), (2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 5$ |
2B, 5B.1.4[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$3.130278287$ |
1.399903007 |
\( -\frac{24389}{12} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -3\) , \( -3\bigr] \) |
${y}^2+{x}{y}={x}^{3}-3{x}-3$ |
| 2304.1-i1 |
2304.1-i |
$4$ |
$10$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{28} \cdot 3^{2} \) |
$1.38434$ |
$(2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$4.402242811$ |
1.968742835 |
\( -\frac{24389}{12} \) |
\( \bigl[0\) , \( -\phi - 1\) , \( 0\) , \( \phi - 9\) , \( 17 \phi - 4\bigr] \) |
${y}^2={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(\phi-9\right){x}+17\phi-4$ |
| 2304.1-l1 |
2304.1-l |
$4$ |
$10$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{28} \cdot 3^{2} \) |
$1.38434$ |
$(2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$4.402242811$ |
1.968742835 |
\( -\frac{24389}{12} \) |
\( \bigl[0\) , \( \phi + 1\) , \( 0\) , \( \phi - 9\) , \( -17 \phi + 4\bigr] \) |
${y}^2={x}^{3}+\left(\phi+1\right){x}^{2}+\left(\phi-9\right){x}-17\phi+4$ |
| 2304.1-q1 |
2304.1-q |
$4$ |
$10$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{28} \cdot 3^{2} \) |
$1.38434$ |
$(2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$1.749878759$ |
0.782569571 |
\( -\frac{24389}{12} \) |
\( \bigl[0\) , \( -\phi + 1\) , \( 0\) , \( -10 \phi - 9\) , \( -25 \phi - 21\bigr] \) |
${y}^2={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(-10\phi-9\right){x}-25\phi-21$ |
| 4356.2-l1 |
4356.2-l |
$4$ |
$10$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4356.2 |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 11^{6} \) |
$1.62329$ |
$(-3a+2), (2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$5.309304596$ |
2.374393198 |
\( -\frac{24389}{12} \) |
\( \bigl[\phi\) , \( 1\) , \( \phi + 1\) , \( -5 \phi - 6\) , \( 9 \phi + 1\bigr] \) |
${y}^2+\phi{x}{y}+\left(\phi+1\right){y}={x}^{3}+{x}^{2}+\left(-5\phi-6\right){x}+9\phi+1$ |
| 4356.3-l1 |
4356.3-l |
$4$ |
$10$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4356.3 |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 11^{6} \) |
$1.62329$ |
$(-3a+1), (2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$5.309304596$ |
2.374393198 |
\( -\frac{24389}{12} \) |
\( \bigl[\phi + 1\) , \( -\phi + 1\) , \( \phi\) , \( 3 \phi - 10\) , \( -10 \phi + 11\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(3\phi-10\right){x}-10\phi+11$ |
*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.
