| 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 |
| 32.1-a1 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$0.60113$ |
$(a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$6.875185818$ |
0.607686314 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}$ |
| 32.1-a2 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$0.60113$ |
$(a)$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$6.875185818$ |
0.607686314 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}$ |
| 1024.1-b1 |
1024.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$1.42974$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.608709031$ |
$4.861490513$ |
2.092493851 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( 0\bigr] \) |
${y}^2={x}^{3}-2{x}$ |
| 1024.1-b2 |
1024.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$1.42974$ |
$(a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1.217418063$ |
$4.861490513$ |
2.092493851 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+2{x}$ |
| 2304.1-b1 |
2304.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$1.75107$ |
$(a), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$3.969390382$ |
1.403391428 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 a - 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(2a-1\right){x}$ |
| 2304.1-b2 |
2304.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$1.75107$ |
$(a), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$3.969390382$ |
1.403391428 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 a + 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-2a+1\right){x}$ |
| 2304.3-b1 |
2304.3-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2304.3 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$1.75107$ |
$(a), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$3.969390382$ |
1.403391428 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 a - 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-2a-1\right){x}$ |
| 2304.3-b2 |
2304.3-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2304.3 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$1.75107$ |
$(a), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$3.969390382$ |
1.403391428 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 a + 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(2a+1\right){x}$ |
| 2592.3-c1 |
2592.3-c |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{6} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$0.250591196$ |
$3.969390382$ |
2.813420292 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -3\) , \( 0\bigr] \) |
${y}^2={x}^{3}-3{x}$ |
| 2592.3-c2 |
2592.3-c |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{6} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$0.125295598$ |
$3.969390382$ |
2.813420292 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+3{x}$ |
| 2592.3-d1 |
2592.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{12} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$0.444312937$ |
$2.291728606$ |
2.880030840 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 9\) , \( 0\bigr] \) |
${y}^2={x}^{3}+9{x}$ |
| 2592.3-d2 |
2592.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{12} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.222156468$ |
$2.291728606$ |
2.880030840 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -9\) , \( 0\bigr] \) |
${y}^2={x}^{3}-9{x}$ |
| 2592.3-e1 |
2592.3-e |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{18} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$1.323130127$ |
1.871188571 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -27\) , \( 0\bigr] \) |
${y}^2={x}^{3}-27{x}$ |
| 2592.3-e2 |
2592.3-e |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{18} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$1.323130127$ |
1.871188571 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 27\) , \( 0\bigr] \) |
${y}^2={x}^{3}+27{x}$ |
| 9216.1-d1 |
9216.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.1 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{6} \) |
$2.47639$ |
$(a), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$0.458003790$ |
$2.806782856$ |
3.635991684 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a + 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-4a+2\right){x}$ |
| 9216.1-d2 |
9216.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.1 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{6} \) |
$2.47639$ |
$(a), (-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.916007581$ |
$2.806782856$ |
3.635991684 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a - 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(4a-2\right){x}$ |
| 9216.3-d1 |
9216.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.3 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{6} \) |
$2.47639$ |
$(a), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$0.458003790$ |
$2.806782856$ |
3.635991684 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a + 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(4a+2\right){x}$ |
| 9216.3-d2 |
9216.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.3 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{6} \) |
$2.47639$ |
$(a), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.916007581$ |
$2.806782856$ |
3.635991684 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a - 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-4a-2\right){x}$ |
| 9248.1-a1 |
9248.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9248.1 |
\( 2^{5} \cdot 17^{2} \) |
\( 2^{12} \cdot 17^{6} \) |
$2.47854$ |
$(a), (-2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$0.719213649$ |
$1.667477489$ |
3.392055068 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -12 a + 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-12a+1\right){x}$ |
| 9248.1-a2 |
9248.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9248.1 |
\( 2^{5} \cdot 17^{2} \) |
\( 2^{12} \cdot 17^{6} \) |
$2.47854$ |
$(a), (-2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.438427298$ |
$1.667477489$ |
3.392055068 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 12 a - 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(12a-1\right){x}$ |
| 9248.3-a1 |
9248.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9248.3 |
\( 2^{5} \cdot 17^{2} \) |
\( 2^{12} \cdot 17^{6} \) |
$2.47854$ |
$(a), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$0.719213649$ |
$1.667477489$ |
3.392055068 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 12 a + 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(12a+1\right){x}$ |
| 9248.3-a2 |
9248.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9248.3 |
\( 2^{5} \cdot 17^{2} \) |
\( 2^{12} \cdot 17^{6} \) |
$2.47854$ |
$(a), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.438427298$ |
$1.667477489$ |
3.392055068 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -12 a - 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-12a-1\right){x}$ |
| 16384.1-a1 |
16384.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
16384.1 |
\( 2^{14} \) |
\( 2^{21} \) |
$2.85949$ |
$(a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1.012804378$ |
$4.088009945$ |
5.855345308 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 a\) , \( 0\bigr] \) |
${y}^2={x}^{3}+2a{x}$ |
| 16384.1-a2 |
16384.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
16384.1 |
\( 2^{14} \) |
\( 2^{21} \) |
$2.85949$ |
$(a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1.012804378$ |
$4.088009945$ |
5.855345308 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 a\) , \( 0\bigr] \) |
${y}^2={x}^{3}-2a{x}$ |
| 16384.1-b1 |
16384.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
16384.1 |
\( 2^{14} \) |
\( 2^{15} \) |
$2.85949$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$5.781319108$ |
2.044004972 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -a\) , \( 0\bigr] \) |
${y}^2={x}^{3}-a{x}$ |
| 16384.1-b2 |
16384.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
16384.1 |
\( 2^{14} \) |
\( 2^{15} \) |
$2.85949$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$5.781319108$ |
2.044004972 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( a\) , \( 0\bigr] \) |
${y}^2={x}^{3}+a{x}$ |
| 20000.1-f1 |
20000.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20000.1 |
\( 2^{5} \cdot 5^{4} \) |
\( 2^{12} \cdot 5^{6} \) |
$3.00567$ |
$(a), (5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.713078665$ |
$3.074676569$ |
6.201287618 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 5\) , \( 0\bigr] \) |
${y}^2={x}^{3}+5{x}$ |
| 20000.1-f2 |
20000.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20000.1 |
\( 2^{5} \cdot 5^{4} \) |
\( 2^{12} \cdot 5^{6} \) |
$3.00567$ |
$(a), (5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.713078665$ |
$3.074676569$ |
6.201287618 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -5\) , \( 0\bigr] \) |
${y}^2={x}^{3}-5{x}$ |
| 20000.1-g1 |
20000.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20000.1 |
\( 2^{5} \cdot 5^{4} \) |
\( 2^{12} \cdot 5^{12} \) |
$3.00567$ |
$(a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$0.949741086$ |
$1.375037163$ |
3.693725825 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 25\) , \( 0\bigr] \) |
${y}^2={x}^{3}+25{x}$ |
| 20000.1-g2 |
20000.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20000.1 |
\( 2^{5} \cdot 5^{4} \) |
\( 2^{12} \cdot 5^{12} \) |
$3.00567$ |
$(a), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.899482172$ |
$1.375037163$ |
3.693725825 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -25\) , \( 0\bigr] \) |
${y}^2={x}^{3}-25{x}$ |
| 20000.1-h1 |
20000.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20000.1 |
\( 2^{5} \cdot 5^{4} \) |
\( 2^{12} \cdot 5^{18} \) |
$3.00567$ |
$(a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$4.982067391$ |
$0.614935313$ |
4.332654213 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 125\) , \( 0\bigr] \) |
${y}^2={x}^{3}+125{x}$ |
| 20000.1-h2 |
20000.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20000.1 |
\( 2^{5} \cdot 5^{4} \) |
\( 2^{12} \cdot 5^{18} \) |
$3.00567$ |
$(a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$2.491033695$ |
$0.614935313$ |
4.332654213 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -125\) , \( 0\bigr] \) |
${y}^2={x}^{3}-125{x}$ |
| 20736.3-j1 |
20736.3-j |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{12} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$0.711675809$ |
$2.291728606$ |
4.613073595 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -6 a - 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-6a-3\right){x}$ |
| 20736.3-j2 |
20736.3-j |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{12} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1.423351618$ |
$2.291728606$ |
4.613073595 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 6 a + 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(6a+3\right){x}$ |
| 20736.3-q1 |
20736.3-q |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{12} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$0.711675809$ |
$2.291728606$ |
4.613073595 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 6 a - 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(6a-3\right){x}$ |
| 20736.3-q2 |
20736.3-q |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{12} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1.423351618$ |
$2.291728606$ |
4.613073595 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -6 a + 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-6a+3\right){x}$ |
| 30976.1-d1 |
30976.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
30976.1 |
\( 2^{8} \cdot 11^{2} \) |
\( 2^{12} \cdot 11^{6} \) |
$3.35305$ |
$(a), (a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$2.072946520$ |
0.732897270 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -6 a - 7\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-6a-7\right){x}$ |
| 30976.1-d2 |
30976.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
30976.1 |
\( 2^{8} \cdot 11^{2} \) |
\( 2^{12} \cdot 11^{6} \) |
$3.35305$ |
$(a), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$2.072946520$ |
0.732897270 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 6 a + 7\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(6a+7\right){x}$ |
| 30976.3-d1 |
30976.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
30976.3 |
\( 2^{8} \cdot 11^{2} \) |
\( 2^{12} \cdot 11^{6} \) |
$3.35305$ |
$(a), (a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$2.072946520$ |
0.732897270 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 6 a - 7\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(6a-7\right){x}$ |
| 30976.3-d2 |
30976.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
30976.3 |
\( 2^{8} \cdot 11^{2} \) |
\( 2^{12} \cdot 11^{6} \) |
$3.35305$ |
$(a), (a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$2.072946520$ |
0.732897270 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -6 a + 7\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-6a+7\right){x}$ |
| 34848.1-d1 |
34848.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
34848.1 |
\( 2^{5} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{12} \cdot 3^{9} \cdot 11^{9} \) |
$3.45325$ |
$(a), (-a-1), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$3.387114386$ |
$0.499343022$ |
4.783809120 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -116 a - 95\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-116a-95\right){x}$ |
| 34848.1-d2 |
34848.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
34848.1 |
\( 2^{5} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{12} \cdot 3^{9} \cdot 11^{9} \) |
$3.45325$ |
$(a), (-a-1), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$1.693557193$ |
$0.499343022$ |
4.783809120 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 116 a + 95\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(116a+95\right){x}$ |
| 34848.1-e1 |
34848.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
34848.1 |
\( 2^{5} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{12} \cdot 3^{6} \cdot 11^{6} \) |
$3.45325$ |
$(a), (-a-1), (a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.196816231$ |
1.692553746 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -8 a + 31\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-8a+31\right){x}$ |
| 34848.1-e2 |
34848.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
34848.1 |
\( 2^{5} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{12} \cdot 3^{6} \cdot 11^{6} \) |
$3.45325$ |
$(a), (-a-1), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$1.196816231$ |
1.692553746 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 8 a - 31\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(8a-31\right){x}$ |
| 34848.1-h1 |
34848.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
34848.1 |
\( 2^{5} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{12} \cdot 3^{3} \cdot 11^{3} \) |
$3.45325$ |
$(a), (-a-1), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$0.550038931$ |
$2.868507274$ |
4.462665945 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a + 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(4a+1\right){x}$ |
| 34848.1-h2 |
34848.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
34848.1 |
\( 2^{5} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{12} \cdot 3^{3} \cdot 11^{3} \) |
$3.45325$ |
$(a), (-a-1), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$0.275019465$ |
$2.868507274$ |
4.462665945 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a - 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-4a-1\right){x}$ |
| 34848.3-a1 |
34848.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
34848.3 |
\( 2^{5} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{12} \cdot 3^{3} \cdot 11^{9} \) |
$3.45325$ |
$(a), (-a-1), (a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$0.864887485$ |
1.223135611 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -16 a + 59\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-16a+59\right){x}$ |
| 34848.3-a2 |
34848.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
34848.3 |
\( 2^{5} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{12} \cdot 3^{3} \cdot 11^{9} \) |
$3.45325$ |
$(a), (-a-1), (a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$0.864887485$ |
1.223135611 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 16 a - 59\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(16a-59\right){x}$ |
| 34848.3-b1 |
34848.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
34848.3 |
\( 2^{5} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{12} \cdot 3^{9} \cdot 11^{3} \) |
$3.45325$ |
$(a), (-a-1), (a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$0.509976775$ |
$1.656133446$ |
4.777720236 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 8 a - 13\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(8a-13\right){x}$ |
| 34848.3-b2 |
34848.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
34848.3 |
\( 2^{5} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{12} \cdot 3^{9} \cdot 11^{3} \) |
$3.45325$ |
$(a), (-a-1), (a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1.019953550$ |
$1.656133446$ |
4.777720236 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -8 a + 13\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-8a+13\right){x}$ |
*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.
