| 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 |
| 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 |
\( -\frac{24389}{12} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -3\) , \( -3\bigr] \) |
${y}^2+{x}{y}={x}^{3}-3{x}-3$ |
| 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 |
\( -\frac{19465109}{248832} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -28\) , \( 272\bigr] \) |
${y}^2+{x}{y}={x}^{3}-28{x}+272$ |
| 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 |
\( \frac{502270291349}{1889568} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -828\) , \( 9072\bigr] \) |
${y}^2+{x}{y}={x}^{3}-828{x}+9072$ |
| 900.1-a4 |
900.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 5^{6} \) |
$1.09442$ |
$(-2a+1), (2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 5$ |
2B, 5B.1.4[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$3.130278287$ |
1.399903007 |
\( \frac{131872229}{18} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -53\) , \( -153\bigr] \) |
${y}^2+{x}{y}={x}^{3}-53{x}-153$ |
| 900.1-b1 |
900.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{2} \cdot 5^{12} \) |
$1.09442$ |
$(-2a+1), (2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.400414114$ |
1.073497826 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[\phi\) , \( -1\) , \( 1\) , \( 67 \phi - 135\) , \( -1275 \phi + 2231\bigr] \) |
${y}^2+\phi{x}{y}+{y}={x}^{3}-{x}^{2}+\left(67\phi-135\right){x}-1275\phi+2231$ |
| 900.1-b2 |
900.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{8} \) |
$1.09442$ |
$(-2a+1), (2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.400414114$ |
1.073497826 |
\( \frac{357911}{2160} \) |
\( \bigl[\phi\) , \( -1\) , \( 1\) , \( -8 \phi + 15\) , \( 45 \phi - 79\bigr] \) |
${y}^2+\phi{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-8\phi+15\right){x}+45\phi-79$ |
| 900.1-b3 |
900.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{2} \cdot 5^{30} \) |
$1.09442$ |
$(-2a+1), (2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.600103528$ |
1.073497826 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[\phi\) , \( -1\) , \( 1\) , \( 2267 \phi - 4535\) , \( -10875 \phi + 19031\bigr] \) |
${y}^2+\phi{x}{y}+{y}={x}^{3}-{x}^{2}+\left(2267\phi-4535\right){x}-10875\phi+19031$ |
| 900.1-b4 |
900.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{24} \cdot 5^{8} \) |
$1.09442$ |
$(-2a+1), (2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.400414114$ |
1.073497826 |
\( \frac{35578826569}{5314410} \) |
\( \bigl[\phi + 1\) , \( -\phi - 1\) , \( 1\) , \( -343 \phi - 343\) , \( 3875 \phi + 2906\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-343\phi-343\right){x}+3875\phi+2906$ |
| 900.1-b5 |
900.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 5^{10} \) |
$1.09442$ |
$(-2a+1), (2), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.400414114$ |
1.073497826 |
\( \frac{702595369}{72900} \) |
\( \bigl[\phi + 1\) , \( -\phi - 1\) , \( 1\) , \( -93 \phi - 93\) , \( -525 \phi - 394\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-93\phi-93\right){x}-525\phi-394$ |
| 900.1-b6 |
900.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{18} \) |
$1.09442$ |
$(-2a+1), (2), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.400414114$ |
1.073497826 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[\phi + 1\) , \( -\phi - 1\) , \( 1\) , \( -1668 \phi - 1668\) , \( 47355 \phi + 35516\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-1668\phi-1668\right){x}+47355\phi+35516$ |
| 900.1-b7 |
900.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{6} \cdot 5^{14} \) |
$1.09442$ |
$(-2a+1), (2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.600103528$ |
1.073497826 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[\phi + 1\) , \( -\phi - 1\) , \( 1\) , \( -1443 \phi - 1443\) , \( -37245 \phi - 27934\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-1443\phi-1443\right){x}-37245\phi-27934$ |
| 900.1-b8 |
900.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{8} \cdot 5^{12} \) |
$1.09442$ |
$(-2a+1), (2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.400414114$ |
1.073497826 |
\( \frac{16778985534208729}{81000} \) |
\( \bigl[\phi + 1\) , \( -\phi - 1\) , \( 1\) , \( -26668 \phi - 26668\) , \( 3007355 \phi + 2255516\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-26668\phi-26668\right){x}+3007355\phi+2255516$ |
*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.
