| 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 |
| 50625.3-CMf1 |
50625.3-CMf |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50625.3 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{18} \cdot 5^{9} \) |
$2.68077$ |
$(-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-4$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$1$ |
$0.791416409$ |
3.165665637 |
\( 1728 \) |
\( \bigl[i + 1\) , \( i\) , \( 1\) , \( 67 i - 35\) , \( -17 i - 34\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(67i-35\right){x}-17i-34$ |
| 50625.3-CMe1 |
50625.3-CMe |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50625.3 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{18} \cdot 5^{9} \) |
$2.68077$ |
$(-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-4$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$1$ |
$0.791416409$ |
3.165665637 |
\( 1728 \) |
\( \bigl[i + 1\) , \( i\) , \( i\) , \( -68 i - 34\) , \( -17 i + 34\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(-68i-34\right){x}-17i+34$ |
| 50625.3-CMd1 |
50625.3-CMd |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50625.3 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{12} \cdot 5^{15} \) |
$2.68077$ |
$(-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-4$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$5$ |
5Cs.4.1 |
$1$ |
\( 2^{3} \) |
$1$ |
$0.613028514$ |
1.226057029 |
\( 1728 \) |
\( \bigl[i + 1\) , \( i\) , \( 1\) , \( -113 i + 55\) , \( 28 i + 56\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(-113i+55\right){x}+28i+56$ |
| 50625.3-CMc1 |
50625.3-CMc |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50625.3 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{12} \cdot 5^{15} \) |
$2.68077$ |
$(-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-4$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$5$ |
5Cs.4.1 |
$1$ |
\( 2^{3} \) |
$1$ |
$0.613028514$ |
1.226057029 |
\( 1728 \) |
\( \bigl[i + 1\) , \( i\) , \( i\) , \( 112 i + 56\) , \( 28 i - 56\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(112i+56\right){x}+28i-56$ |
| 50625.3-CMb1 |
50625.3-CMb |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50625.3 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{6} \cdot 5^{9} \) |
$2.68077$ |
$(-a-2), (2a+1), (3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-4$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$0.081821379$ |
$2.374249228$ |
3.108229546 |
\( 1728 \) |
\( \bigl[i + 1\) , \( i\) , \( 1\) , \( 7 i - 5\) , \( -2 i - 4\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(7i-5\right){x}-2i-4$ |
| 50625.3-CMa1 |
50625.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50625.3 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{6} \cdot 5^{9} \) |
$2.68077$ |
$(-a-2), (2a+1), (3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-4$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$0.081821379$ |
$2.374249228$ |
3.108229546 |
\( 1728 \) |
\( \bigl[i + 1\) , \( i\) , \( i\) , \( -8 i - 4\) , \( -2 i + 4\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(-8i-4\right){x}-2i+4$ |
| 50625.3-a1 |
50625.3-a |
$2$ |
$5$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50625.3 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{14} \cdot 5^{8} \) |
$2.68077$ |
$(-a-2), (2a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.025588090$ |
$1.091534363$ |
2.010980162 |
\( -\frac{102400}{3} \) |
\( \bigl[0\) , \( 0\) , \( i\) , \( -75\) , \( -256\bigr] \) |
${y}^2+i{y}={x}^{3}-75{x}-256$ |
| 50625.3-a2 |
50625.3-a |
$2$ |
$5$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50625.3 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{22} \cdot 5^{16} \) |
$2.68077$ |
$(-a-2), (2a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.127940452$ |
$0.218306872$ |
2.010980162 |
\( \frac{20480}{243} \) |
\( \bigl[0\) , \( 0\) , \( i\) , \( 375\) , \( 12344\bigr] \) |
${y}^2+i{y}={x}^{3}+375{x}+12344$ |
| 50625.3-b1 |
50625.3-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50625.3 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{14} \cdot 5^{32} \) |
$2.68077$ |
$(-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$2.400975354$ |
$0.037261695$ |
2.862861179 |
\( -\frac{117751185817608007}{457763671875} a - \frac{2360548126387992}{152587890625} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -23625 i + 88871\) , \( -9922500 i - 4089872\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}+\left(-23625i+88871\right){x}-9922500i-4089872$ |
| 50625.3-b2 |
50625.3-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50625.3 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{14} \cdot 5^{32} \) |
$2.68077$ |
$(-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$2.400975354$ |
$0.037261695$ |
2.862861179 |
\( \frac{117751185817608007}{457763671875} a - \frac{2360548126387992}{152587890625} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( 23625 i + 88871\) , \( 9922500 i - 4089872\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}+\left(23625i+88871\right){x}+9922500i-4089872$ |
| 50625.3-b3 |
50625.3-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50625.3 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{44} \cdot 5^{14} \) |
$2.68077$ |
$(-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$9.603901418$ |
$0.037261695$ |
2.862861179 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -24754\) , \( -2820872\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-24754{x}-2820872$ |
| 50625.3-b4 |
50625.3-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50625.3 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{14} \cdot 5^{14} \) |
$2.68077$ |
$(-a-2), (2a+1), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.600243838$ |
$0.596187123$ |
2.862861179 |
\( -\frac{1}{15} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -4\) , \( 628\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-4{x}+628$ |
| 50625.3-b5 |
50625.3-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50625.3 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{16} \cdot 5^{28} \) |
$2.68077$ |
$(-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$4.801950709$ |
$0.074523390$ |
2.862861179 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( 7871\) , \( -141122\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}+7871{x}-141122$ |
| 50625.3-b6 |
50625.3-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50625.3 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{20} \cdot 5^{20} \) |
$2.68077$ |
$(-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$2.400975354$ |
$0.149046780$ |
2.862861179 |
\( \frac{111284641}{50625} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -2254\) , \( -19622\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-2254{x}-19622$ |
| 50625.3-b7 |
50625.3-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50625.3 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{16} \cdot 5^{16} \) |
$2.68077$ |
$(-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1.200487677$ |
$0.298093561$ |
2.862861179 |
\( \frac{13997521}{225} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -1129\) , \( 14128\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-1129{x}+14128$ |
| 50625.3-b8 |
50625.3-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50625.3 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{28} \cdot 5^{16} \) |
$2.68077$ |
$(-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$4.801950709$ |
$0.074523390$ |
2.862861179 |
\( \frac{272223782641}{164025} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -30379\) , \( -2044622\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-30379{x}-2044622$ |
| 50625.3-b9 |
50625.3-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50625.3 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{14} \cdot 5^{14} \) |
$2.68077$ |
$(-a-2), (2a+1), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$2.400975354$ |
$0.149046780$ |
2.862861179 |
\( \frac{56667352321}{15} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -18004\) , \( 925378\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-18004{x}+925378$ |
| 50625.3-b10 |
50625.3-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50625.3 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{20} \cdot 5^{14} \) |
$2.68077$ |
$(-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$9.603901418$ |
$0.037261695$ |
2.862861179 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -486004\) , \( -130530872\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-486004{x}-130530872$ |
| 50625.3-c1 |
50625.3-c |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50625.3 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{18} \cdot 5^{4} \) |
$2.68077$ |
$(-a-2), (2a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$5$ |
5Ns.2.1 |
$1$ |
\( 2 \) |
$0.460920105$ |
$1.580651525$ |
2.914216267 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( i\) , \( 0\) , \( 34\bigr] \) |
${y}^2+i{y}={x}^{3}+34$ |
| 50625.3-c2 |
50625.3-c |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50625.3 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{6} \cdot 5^{4} \) |
$2.68077$ |
$(-a-2), (2a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$5$ |
5Ns.2.1 |
$1$ |
\( 2 \) |
$0.153640035$ |
$4.741954575$ |
2.914216267 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( i\) , \( 0\) , \( -1\bigr] \) |
${y}^2+i{y}={x}^{3}-1$ |
| 50625.3-d1 |
50625.3-d |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50625.3 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{18} \cdot 5^{17} \) |
$2.68077$ |
$(-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1.897634689$ |
$0.207768522$ |
3.154150045 |
\( -\frac{8722944}{125} a - \frac{10158912}{125} \) |
\( \bigl[i + 1\) , \( i\) , \( i\) , \( -338 i + 2531\) , \( -47672 i - 9956\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(-338i+2531\right){x}-47672i-9956$ |
| 50625.3-d2 |
50625.3-d |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50625.3 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{6} \cdot 5^{17} \) |
$2.68077$ |
$(-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$0.316272448$ |
$0.623305567$ |
3.154150045 |
\( \frac{8722944}{125} a - \frac{10158912}{125} \) |
\( \bigl[i + 1\) , \( i\) , \( 1\) , \( 37 i + 280\) , \( 1953 i - 394\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(37i+280\right){x}+1953i-394$ |
| 50625.3-d3 |
50625.3-d |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50625.3 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{6} \cdot 5^{19} \) |
$2.68077$ |
$(-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.632544896$ |
$0.623305567$ |
3.154150045 |
\( -\frac{5792256}{15625} a + \frac{13929408}{15625} \) |
\( \bigl[i + 1\) , \( i\) , \( i\) , \( 37 i - 94\) , \( -422 i - 81\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(37i-94\right){x}-422i-81$ |
| 50625.3-d4 |
50625.3-d |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50625.3 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{18} \cdot 5^{19} \) |
$2.68077$ |
$(-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$0.948817344$ |
$0.207768522$ |
3.154150045 |
\( \frac{5792256}{15625} a + \frac{13929408}{15625} \) |
\( \bigl[i + 1\) , \( i\) , \( 1\) , \( -338 i - 845\) , \( 9703 i - 1519\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(-338i-845\right){x}+9703i-1519$ |
| 50625.3-e1 |
50625.3-e |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50625.3 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{6} \cdot 5^{17} \) |
$2.68077$ |
$(-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$0.316272448$ |
$0.623305567$ |
3.154150045 |
\( -\frac{8722944}{125} a - \frac{10158912}{125} \) |
\( \bigl[i + 1\) , \( i\) , \( i\) , \( -38 i + 281\) , \( -1672 i - 356\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(-38i+281\right){x}-1672i-356$ |
| 50625.3-e2 |
50625.3-e |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50625.3 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{18} \cdot 5^{17} \) |
$2.68077$ |
$(-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1.897634689$ |
$0.207768522$ |
3.154150045 |
\( \frac{8722944}{125} a - \frac{10158912}{125} \) |
\( \bigl[i + 1\) , \( i\) , \( 1\) , \( 337 i + 2530\) , \( -47672 i + 9956\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(337i+2530\right){x}-47672i+9956$ |
| 50625.3-e3 |
50625.3-e |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50625.3 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{18} \cdot 5^{19} \) |
$2.68077$ |
$(-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$0.948817344$ |
$0.207768522$ |
3.154150045 |
\( -\frac{5792256}{15625} a + \frac{13929408}{15625} \) |
\( \bigl[i + 1\) , \( i\) , \( i\) , \( 337 i - 844\) , \( -10547 i - 1856\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(337i-844\right){x}-10547i-1856$ |
| 50625.3-e4 |
50625.3-e |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50625.3 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{6} \cdot 5^{19} \) |
$2.68077$ |
$(-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.632544896$ |
$0.623305567$ |
3.154150045 |
\( \frac{5792256}{15625} a + \frac{13929408}{15625} \) |
\( \bigl[i + 1\) , \( i\) , \( 1\) , \( -38 i - 95\) , \( -422 i + 81\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(-38i-95\right){x}-422i+81$ |
| 50625.3-f1 |
50625.3-f |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50625.3 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{6} \cdot 5^{16} \) |
$2.68077$ |
$(-a-2), (2a+1), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3, 5$ |
3B.1.1, 5Ns.2.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1.007478452$ |
$0.948390915$ |
3.821933646 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 156\bigr] \) |
${y}^2+{y}={x}^{3}+156$ |
| 50625.3-f2 |
50625.3-f |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50625.3 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{18} \cdot 5^{16} \) |
$2.68077$ |
$(-a-2), (2a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3, 5$ |
3B.1.2, 5Ns.2.1 |
$1$ |
\( 2 \) |
$3.022435358$ |
$0.316130305$ |
3.821933646 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -4219\bigr] \) |
${y}^2+{y}={x}^{3}-4219$ |
| 50625.3-g1 |
50625.3-g |
$2$ |
$5$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50625.3 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{14} \cdot 5^{20} \) |
$2.68077$ |
$(-a-2), (2a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2^{2} \) |
$4.591654055$ |
$0.218306872$ |
8.019117100 |
\( -\frac{102400}{3} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -1875\) , \( 32031\bigr] \) |
${y}^2+{y}={x}^{3}-1875{x}+32031$ |
| 50625.3-g2 |
50625.3-g |
$2$ |
$5$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50625.3 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{22} \cdot 5^{4} \) |
$2.68077$ |
$(-a-2), (2a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2^{2} \) |
$0.918330811$ |
$1.091534363$ |
8.019117100 |
\( \frac{20480}{243} \) |
\( \bigl[0\) , \( 0\) , \( i\) , \( 15\) , \( 99\bigr] \) |
${y}^2+i{y}={x}^{3}+15{x}+99$ |
*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.
