| 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 |
| 2025.1-a1 |
2025.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{14} \cdot 5^{8} \) |
$1.34039$ |
$(-2a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.4.1[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.025588090$ |
$7.268178697$ |
1.996134097 |
\( -\frac{102400}{3} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -75\) , \( 256\bigr] \) |
${y}^2+{y}={x}^{3}-75{x}+256$ |
| 2025.1-a2 |
2025.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{22} \cdot 5^{4} \) |
$1.34039$ |
$(-2a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.4.1[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.127940452$ |
$1.453635739$ |
1.996134097 |
\( \frac{20480}{243} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 15\) , \( -99\bigr] \) |
${y}^2+{y}={x}^{3}+15{x}-99$ |
| 2025.1-b1 |
2025.1-b |
$10$ |
$32$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( - 3^{16} \cdot 5^{7} \) |
$1.34039$ |
$(-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$64$ |
\( 2^{4} \) |
$1$ |
$0.018276957$ |
2.092468141 |
\( -\frac{152409672113485069453847362}{45} a + \frac{246604029693845863366701161}{45} \) |
\( \bigl[\phi + 1\) , \( 1\) , \( 0\) , \( 151875 \phi - 500175\) , \( 56696050 \phi - 141391500\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+{x}^{2}+\left(151875\phi-500175\right){x}+56696050\phi-141391500$ |
| 2025.1-b2 |
2025.1-b |
$10$ |
$32$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{44} \cdot 5^{8} \) |
$1.34039$ |
$(-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 2^{4} \) |
$1$ |
$0.073107828$ |
2.092468141 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[\phi + 1\) , \( 1\) , \( 0\) , \( -4950 \phi - 4950\) , \( -455300 \phi - 341475\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-4950\phi-4950\right){x}-455300\phi-341475$ |
| 2025.1-b3 |
2025.1-b |
$10$ |
$32$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{14} \cdot 5^{8} \) |
$1.34039$ |
$(-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.678901004$ |
2.092468141 |
\( -\frac{1}{15} \) |
\( \bigl[\phi + 1\) , \( 1\) , \( 0\) , \( 0\) , \( 100 \phi + 75\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+{x}^{2}+100\phi+75$ |
| 2025.1-b4 |
2025.1-b |
$10$ |
$32$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{16} \cdot 5^{22} \) |
$1.34039$ |
$(-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.292431312$ |
2.092468141 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[\phi + 1\) , \( 1\) , \( 0\) , \( 1575 \phi + 1575\) , \( -21320 \phi - 15990\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+{x}^{2}+\left(1575\phi+1575\right){x}-21320\phi-15990$ |
| 2025.1-b5 |
2025.1-b |
$10$ |
$32$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{20} \cdot 5^{14} \) |
$1.34039$ |
$(-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$1.169725251$ |
2.092468141 |
\( \frac{111284641}{50625} \) |
\( \bigl[\phi + 1\) , \( 1\) , \( 0\) , \( -450 \phi - 450\) , \( -3500 \phi - 2625\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-450\phi-450\right){x}-3500\phi-2625$ |
| 2025.1-b6 |
2025.1-b |
$10$ |
$32$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{16} \cdot 5^{10} \) |
$1.34039$ |
$(-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$4.678901004$ |
2.092468141 |
\( \frac{13997521}{225} \) |
\( \bigl[\phi + 1\) , \( 1\) , \( 0\) , \( -225 \phi - 225\) , \( 2080 \phi + 1560\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-225\phi-225\right){x}+2080\phi+1560$ |
| 2025.1-b7 |
2025.1-b |
$10$ |
$32$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{28} \cdot 5^{10} \) |
$1.34039$ |
$(-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$16$ |
\( 2^{4} \) |
$1$ |
$0.292431312$ |
2.092468141 |
\( \frac{272223782641}{164025} \) |
\( \bigl[\phi + 1\) , \( 1\) , \( 0\) , \( -6075 \phi - 6075\) , \( -332000 \phi - 249000\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-6075\phi-6075\right){x}-332000\phi-249000$ |
| 2025.1-b8 |
2025.1-b |
$10$ |
$32$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{14} \cdot 5^{8} \) |
$1.34039$ |
$(-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.678901004$ |
2.092468141 |
\( \frac{56667352321}{15} \) |
\( \bigl[\phi\) , \( -\phi - 1\) , \( \phi\) , \( 3601 \phi - 7202\) , \( -148781 \phi + 261266\bigr] \) |
${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(3601\phi-7202\right){x}-148781\phi+261266$ |
| 2025.1-b9 |
2025.1-b |
$10$ |
$32$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{20} \cdot 5^{8} \) |
$1.34039$ |
$(-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$64$ |
\( 2^{4} \) |
$1$ |
$0.073107828$ |
2.092468141 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[\phi + 1\) , \( 1\) , \( 0\) , \( -97200 \phi - 97200\) , \( -20962700 \phi - 15722025\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-97200\phi-97200\right){x}-20962700\phi-15722025$ |
| 2025.1-b10 |
2025.1-b |
$10$ |
$32$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( - 3^{16} \cdot 5^{7} \) |
$1.34039$ |
$(-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$64$ |
\( 2^{4} \) |
$1$ |
$0.018276957$ |
2.092468141 |
\( \frac{152409672113485069453847362}{45} a + \frac{94194357580360793912853799}{45} \) |
\( \bigl[\phi\) , \( -\phi - 1\) , \( \phi\) , \( -151874 \phi - 348302\) , \( -56544176 \phi - 84347149\bigr] \) |
${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-151874\phi-348302\right){x}-56544176\phi-84347149$ |
| 2025.1-c1 |
2025.1-c |
$6$ |
$75$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{2} \) |
$1.34039$ |
$(-2a+1), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-75$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5Cs[2] |
$1$ |
\( 2 \) |
$1$ |
$2.448734813$ |
2.190215000 |
\( 292658282496 a - 473531056128 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 6 \phi - 48\) , \( 109 \phi - 76\bigr] \) |
${y}^2+{y}={x}^3+\left(6\phi-48\right){x}+109\phi-76$ |
| 2025.1-c2 |
2025.1-c |
$6$ |
$75$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{18} \cdot 5^{2} \) |
$1.34039$ |
$(-2a+1), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-75$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5Cs[2] |
$1$ |
\( 2 \) |
$1$ |
$2.448734813$ |
2.190215000 |
\( 292658282496 a - 473531056128 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 54 \phi - 432\) , \( -2943 \phi + 2045\bigr] \) |
${y}^2+{y}={x}^3+\left(54\phi-432\right){x}-2943\phi+2045$ |
| 2025.1-c3 |
2025.1-c |
$6$ |
$75$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{2} \) |
$1.34039$ |
$(-2a+1), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-75$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5Cs[2] |
$1$ |
\( 2 \) |
$1$ |
$2.448734813$ |
2.190215000 |
\( -292658282496 a - 180872773632 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -6 \phi - 42\) , \( -109 \phi + 33\bigr] \) |
${y}^2+{y}={x}^3+\left(-6\phi-42\right){x}-109\phi+33$ |
| 2025.1-c4 |
2025.1-c |
$6$ |
$75$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{18} \cdot 5^{2} \) |
$1.34039$ |
$(-2a+1), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-75$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5Cs[2] |
$1$ |
\( 2 \) |
$1$ |
$2.448734813$ |
2.190215000 |
\( -292658282496 a - 180872773632 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -54 \phi - 378\) , \( 2943 \phi - 898\bigr] \) |
${y}^2+{y}={x}^3+\left(-54\phi-378\right){x}+2943\phi-898$ |
| 2025.1-c5 |
2025.1-c |
$6$ |
$75$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{18} \cdot 5^{10} \) |
$1.34039$ |
$(-2a+1), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5Cs[2] |
$1$ |
\( 2 \) |
$1$ |
$2.448734813$ |
2.190215000 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 675 \phi + 506\bigr] \) |
${y}^2+{y}={x}^3+675\phi+506$ |
| 2025.1-c6 |
2025.1-c |
$6$ |
$75$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{10} \) |
$1.34039$ |
$(-2a+1), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5Cs[2] |
$1$ |
\( 2 \) |
$1$ |
$2.448734813$ |
2.190215000 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -25 \phi - 19\bigr] \) |
${y}^2+{y}={x}^3-25\phi-19$ |
| 2025.1-d1 |
2025.1-d |
$6$ |
$75$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{8} \) |
$1.34039$ |
$(-2a+1), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-75$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3, 5$ |
3B.1.2, 5Cs[2] |
$1$ |
\( 2 \cdot 3 \) |
$0.768200175$ |
$3.285322500$ |
1.504894809 |
\( 292658282496 a - 473531056128 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -180 \phi - 210\) , \( -2300 \phi - 1044\bigr] \) |
${y}^2+{y}={x}^3+\left(-180\phi-210\right){x}-2300\phi-1044$ |
| 2025.1-d2 |
2025.1-d |
$6$ |
$75$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{18} \cdot 5^{8} \) |
$1.34039$ |
$(-2a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-75$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3, 5$ |
3B.1.2, 5Cs[2] |
$1$ |
\( 2 \) |
$2.304600525$ |
$0.365035833$ |
1.504894809 |
\( 292658282496 a - 473531056128 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -1620 \phi - 1890\) , \( 62100 \phi + 28181\bigr] \) |
${y}^2+{y}={x}^3+\left(-1620\phi-1890\right){x}+62100\phi+28181$ |
| 2025.1-d3 |
2025.1-d |
$6$ |
$75$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{8} \) |
$1.34039$ |
$(-2a+1), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-75$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3, 5$ |
3B.1.2, 5Cs[2] |
$1$ |
\( 2 \cdot 3 \) |
$0.768200175$ |
$3.285322500$ |
1.504894809 |
\( -292658282496 a - 180872773632 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 180 \phi - 390\) , \( 2300 \phi - 3344\bigr] \) |
${y}^2+{y}={x}^3+\left(180\phi-390\right){x}+2300\phi-3344$ |
| 2025.1-d4 |
2025.1-d |
$6$ |
$75$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{18} \cdot 5^{8} \) |
$1.34039$ |
$(-2a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-75$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3, 5$ |
3B.1.2, 5Cs[2] |
$1$ |
\( 2 \) |
$2.304600525$ |
$0.365035833$ |
1.504894809 |
\( -292658282496 a - 180872773632 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 1620 \phi - 3510\) , \( -62100 \phi + 90281\bigr] \) |
${y}^2+{y}={x}^3+\left(1620\phi-3510\right){x}-62100\phi+90281$ |
| 2025.1-d5 |
2025.1-d |
$6$ |
$75$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{18} \cdot 5^{4} \) |
$1.34039$ |
$(-2a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3, 5$ |
3B.1.2, 5Cs[2] |
$1$ |
\( 2 \) |
$0.460920105$ |
$1.825179167$ |
1.504894809 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -34\bigr] \) |
${y}^2+{y}={x}^3-34$ |
| 2025.1-d6 |
2025.1-d |
$6$ |
$75$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{4} \) |
$1.34039$ |
$(-2a+1), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3, 5$ |
3B.1.2, 5Cs[2] |
$1$ |
\( 2 \cdot 3 \) |
$0.153640035$ |
$16.42661250$ |
1.504894809 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 1\bigr] \) |
${y}^2+{y}={x}^3+1$ |
| 2025.1-e1 |
2025.1-e |
$8$ |
$30$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{6} \) |
$1.34039$ |
$(-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-15$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$3.521839301$ |
1.575014416 |
\( -85995 a - 52515 \) |
\( \bigl[\phi\) , \( -\phi - 1\) , \( 0\) , \( -6 \phi + 6\) , \( -7 \phi + 10\bigr] \) |
${y}^2+\phi{x}{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-6\phi+6\right){x}-7\phi+10$ |
| 2025.1-e2 |
2025.1-e |
$8$ |
$30$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{18} \cdot 5^{6} \) |
$1.34039$ |
$(-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-15$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$3.521839301$ |
1.575014416 |
\( -85995 a - 52515 \) |
\( \bigl[\phi\) , \( -\phi - 1\) , \( 1\) , \( -59 \phi + 51\) , \( 253 \phi - 264\bigr] \) |
${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-59\phi+51\right){x}+253\phi-264$ |
| 2025.1-e3 |
2025.1-e |
$8$ |
$30$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{6} \) |
$1.34039$ |
$(-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-15$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$3.521839301$ |
1.575014416 |
\( 85995 a - 138510 \) |
\( \bigl[\phi + 1\) , \( 1\) , \( \phi + 1\) , \( 6 \phi - 1\) , \( 13 \phi + 2\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+{x}^{2}+\left(6\phi-1\right){x}+13\phi+2$ |
| 2025.1-e4 |
2025.1-e |
$8$ |
$30$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{18} \cdot 5^{6} \) |
$1.34039$ |
$(-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-15$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$3.521839301$ |
1.575014416 |
\( 85995 a - 138510 \) |
\( \bigl[\phi + 1\) , \( 1\) , \( \phi\) , \( 59 \phi - 8\) , \( -194 \phi - 19\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+{x}^{2}+\left(59\phi-8\right){x}-194\phi-19$ |
| 2025.1-e5 |
2025.1-e |
$8$ |
$30$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{6} \) |
$1.34039$ |
$(-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-60$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$3.521839301$ |
1.575014416 |
\( -16554983445 a + 26786530035 \) |
\( \bigl[\phi + 1\) , \( 1\) , \( \phi + 1\) , \( 6 \phi - 76\) , \( 178 \phi - 193\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+{x}^{2}+\left(6\phi-76\right){x}+178\phi-193$ |
| 2025.1-e6 |
2025.1-e |
$8$ |
$30$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{18} \cdot 5^{6} \) |
$1.34039$ |
$(-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-60$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$3.521839301$ |
1.575014416 |
\( -16554983445 a + 26786530035 \) |
\( \bigl[\phi + 1\) , \( 1\) , \( \phi\) , \( 59 \phi - 683\) , \( -5324 \phi + 3896\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+{x}^{2}+\left(59\phi-683\right){x}-5324\phi+3896$ |
| 2025.1-e7 |
2025.1-e |
$8$ |
$30$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{6} \) |
$1.34039$ |
$(-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-60$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$3.521839301$ |
1.575014416 |
\( 16554983445 a + 10231546590 \) |
\( \bigl[\phi\) , \( -\phi - 1\) , \( 0\) , \( -6 \phi - 69\) , \( -172 \phi + 55\bigr] \) |
${y}^2+\phi{x}{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-6\phi-69\right){x}-172\phi+55$ |
| 2025.1-e8 |
2025.1-e |
$8$ |
$30$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{18} \cdot 5^{6} \) |
$1.34039$ |
$(-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-60$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$3.521839301$ |
1.575014416 |
\( 16554983445 a + 10231546590 \) |
\( \bigl[\phi\) , \( -\phi - 1\) , \( 1\) , \( -59 \phi - 624\) , \( 5383 \phi - 804\bigr] \) |
${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-59\phi-624\right){x}+5383\phi-804$ |
| 2025.1-f1 |
2025.1-f |
$2$ |
$5$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{14} \cdot 5^{2} \) |
$1.34039$ |
$(-2a+1), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.1[2] |
$1$ |
\( 2 \) |
$1$ |
$1.466203400$ |
1.311412189 |
\( -\frac{102400}{3} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -15 \phi - 15\) , \( -41 \phi - 31\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-15\phi-15\right){x}-41\phi-31$ |
| 2025.1-f2 |
2025.1-f |
$2$ |
$5$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{22} \cdot 5^{10} \) |
$1.34039$ |
$(-2a+1), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.1[2] |
$1$ |
\( 2 \) |
$1$ |
$1.466203400$ |
1.311412189 |
\( \frac{20480}{243} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -75 \phi + 150\) , \( -1975 \phi + 3456\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-75\phi+150\right){x}-1975\phi+3456$ |
*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.
