| 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 |
| 36864.1-CMb1 |
36864.1-CMb |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{6} \) |
$2.14462$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.554057858$ |
2.949171984 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -8\bigr] \) |
${y}^2={x}^{3}-8$ |
| 36864.1-CMb2 |
36864.1-CMb |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{28} \cdot 3^{6} \) |
$2.14462$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-12$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$1.277028929$ |
2.949171984 |
\( 54000 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -60 a + 60\) , \( -176\bigr] \) |
${y}^2={x}^{3}+\left(-60a+60\right){x}-176$ |
| 36864.1-CMa1 |
36864.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{6} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.320036657$ |
$2.554057858$ |
3.775372582 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 8\bigr] \) |
${y}^2={x}^{3}+8$ |
| 36864.1-CMa2 |
36864.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{28} \cdot 3^{6} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-12$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$0.320036657$ |
$1.277028929$ |
3.775372582 |
\( 54000 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -60\) , \( 176\bigr] \) |
${y}^2={x}^{3}-60{x}+176$ |
| 36864.1-a1 |
36864.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{3} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.227714198$ |
$2.431768399$ |
2.557653340 |
\( 7104 a - 3264 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -11 a + 4\) , \( -6 a + 9\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-11a+4\right){x}-6a+9$ |
| 36864.1-a2 |
36864.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{3} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.455428396$ |
$4.863536798$ |
2.557653340 |
\( -7104 a + 3840 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -a - 1\) , \( 3 a\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-1\right){x}+3a$ |
| 36864.1-b1 |
36864.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{3} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.455428396$ |
$4.863536798$ |
2.557653340 |
\( 7104 a - 3264 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2 a + 2\) , \( 2\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+2\right){x}+2$ |
| 36864.1-b2 |
36864.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{3} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.227714198$ |
$2.431768399$ |
2.557653340 |
\( -7104 a + 3840 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -3 a + 12\) , \( 14 a + 7\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-3a+12\right){x}+14a+7$ |
| 36864.1-c1 |
36864.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{30} \cdot 3^{10} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.384142245$ |
$0.830501854$ |
2.947080732 |
\( \frac{188632}{9} a - \frac{255448}{9} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -115 a + 128\) , \( -58 a - 563\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-115a+128\right){x}-58a-563$ |
| 36864.1-c2 |
36864.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{8} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.768284491$ |
$1.661003709$ |
2.947080732 |
\( \frac{1216}{3} a - 384 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 5 a + 8\) , \( 14 a - 35\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(5a+8\right){x}+14a-35$ |
| 36864.1-c3 |
36864.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{7} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.384142245$ |
$3.322007419$ |
2.947080732 |
\( -\frac{27712}{3} a + \frac{20672}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 5 a - 7\) , \( 5 a - 2\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(5a-7\right){x}+5a-2$ |
| 36864.1-c4 |
36864.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{30} \cdot 3^{7} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.536568983$ |
$0.830501854$ |
2.947080732 |
\( -\frac{2285576}{3} a + \frac{2214136}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 125 a + 128\) , \( 902 a - 1379\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(125a+128\right){x}+902a-1379$ |
| 36864.1-d1 |
36864.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{9} \) |
$2.14462$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2.807964279$ |
1.621178932 |
\( 7104 a - 3264 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 9 a - 3\) , \( -6 a - 4\bigr] \) |
${y}^2={x}^{3}+\left(9a-3\right){x}-6a-4$ |
| 36864.1-d2 |
36864.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{9} \) |
$2.14462$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.403982139$ |
1.621178932 |
\( -7104 a + 3840 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 24 a + 12\) , \( -48 a + 80\bigr] \) |
${y}^2={x}^{3}+\left(24a+12\right){x}-48a+80$ |
| 36864.1-e1 |
36864.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{30} \cdot 3^{14} \) |
$2.14462$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.677048354$ |
1.563576199 |
\( \frac{97336}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 93 a\) , \( -198 a + 99\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+93a{x}-198a+99$ |
| 36864.1-e2 |
36864.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{10} \) |
$2.14462$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.354096709$ |
1.563576199 |
\( \frac{21952}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -27 a\) , \( -54 a + 27\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-27a{x}-54a+27$ |
| 36864.1-e3 |
36864.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{8} \) |
$2.14462$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2.708193418$ |
1.563576199 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -12 a\) , \( 12 a - 6\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-12a{x}+12a-6$ |
| 36864.1-e4 |
36864.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{30} \cdot 3^{8} \) |
$2.14462$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.677048354$ |
1.563576199 |
\( \frac{7301384}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -387 a\) , \( -3654 a + 1827\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-387a{x}-3654a+1827$ |
| 36864.1-f1 |
36864.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{9} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.530494581$ |
$1.403982139$ |
3.440106555 |
\( 7104 a - 3264 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -12 a - 24\) , \( -48 a - 32\bigr] \) |
${y}^2={x}^{3}+\left(-12a-24\right){x}-48a-32$ |
| 36864.1-f2 |
36864.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{9} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.060989162$ |
$2.807964279$ |
3.440106555 |
\( -7104 a + 3840 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 3 a - 9\) , \( -6 a + 10\bigr] \) |
${y}^2={x}^{3}+\left(3a-9\right){x}-6a+10$ |
| 36864.1-g1 |
36864.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{6} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.343244042$ |
$1.897359453$ |
3.008028754 |
\( 1088 a - 3392 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -3 a - 12\) , \( -6 a - 15\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3a-12\right){x}-6a-15$ |
| 36864.1-g2 |
36864.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.686488085$ |
$3.794718906$ |
3.008028754 |
\( -1088 a - 2304 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -3 a + 3\) , \( 3 a - 6\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3a+3\right){x}+3a-6$ |
| 36864.1-h1 |
36864.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.686488085$ |
$3.794718906$ |
3.008028754 |
\( 1088 a - 3392 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 5 a - 1\) , \( a - 4\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(5a-1\right){x}+a-4$ |
| 36864.1-h2 |
36864.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{6} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.343244042$ |
$1.897359453$ |
3.008028754 |
\( -1088 a - 2304 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 5 a - 16\) , \( 10 a - 37\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(5a-16\right){x}+10a-37$ |
| 36864.1-i1 |
36864.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{30} \cdot 3^{7} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.536568983$ |
$0.830501854$ |
2.947080732 |
\( \frac{2285576}{3} a - \frac{71440}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 253 a - 128\) , \( -902 a - 477\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(253a-128\right){x}-902a-477$ |
| 36864.1-i2 |
36864.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{30} \cdot 3^{10} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.384142245$ |
$0.830501854$ |
2.947080732 |
\( -\frac{188632}{9} a - 7424 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 13 a - 128\) , \( 58 a - 621\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(13a-128\right){x}+58a-621$ |
| 36864.1-i3 |
36864.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{7} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.384142245$ |
$3.322007419$ |
2.947080732 |
\( \frac{27712}{3} a - \frac{7040}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2 a + 7\) , \( -5 a + 3\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a+7\right){x}-5a+3$ |
| 36864.1-i4 |
36864.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{8} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.768284491$ |
$1.661003709$ |
2.947080732 |
\( -\frac{1216}{3} a + \frac{64}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 13 a - 8\) , \( -14 a - 21\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(13a-8\right){x}-14a-21$ |
| 36864.1-j1 |
36864.1-j |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{3} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cn[2] |
$1$ |
\( 2 \) |
$0.571185187$ |
$5.224011530$ |
3.445485541 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( a + 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}$ |
| 36864.1-j2 |
36864.1-j |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{3} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cn[2] |
$1$ |
\( 2^{3} \) |
$0.285592593$ |
$2.612005765$ |
3.445485541 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a - 4\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-4a-4\right){x}$ |
| 36864.1-k1 |
36864.1-k |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{9} \) |
$2.14462$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cn[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$1.508042231$ |
1.741337176 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 24 a - 12\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(24a-12\right){x}$ |
| 36864.1-k2 |
36864.1-k |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{9} \) |
$2.14462$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cn[2] |
$1$ |
\( 2 \) |
$1$ |
$3.016084463$ |
1.741337176 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -6 a + 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-6a+3\right){x}$ |
| 36864.1-l1 |
36864.1-l |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{28} \cdot 3^{7} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.348272657$ |
$1.049434289$ |
3.376245242 |
\( \frac{73696}{3} a - \frac{624368}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -67 a + 128\) , \( 346 a + 227\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-67a+128\right){x}+346a+227$ |
| 36864.1-l2 |
36864.1-l |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{28} \cdot 3^{7} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.393090629$ |
$1.049434289$ |
3.376245242 |
\( -\frac{73696}{3} a - \frac{550672}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -127 a + 68\) , \( 286 a - 445\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-127a+68\right){x}+286a-445$ |
| 36864.1-l3 |
36864.1-l |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{34} \cdot 3^{22} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.393090629$ |
$0.262358572$ |
3.376245242 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -187 a + 188\) , \( -8450 a + 4319\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-187a+188\right){x}-8450a+4319$ |
| 36864.1-l4 |
36864.1-l |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{8} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.696545314$ |
$2.098868579$ |
3.376245242 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -7 a + 8\) , \( 10 a - 1\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-7a+8\right){x}+10a-1$ |
| 36864.1-l5 |
36864.1-l |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{28} \cdot 3^{10} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.393090629$ |
$1.049434289$ |
3.376245242 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 53 a - 52\) , \( 142 a - 97\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(53a-52\right){x}+142a-97$ |
| 36864.1-l6 |
36864.1-l |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{32} \cdot 3^{14} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$2.786181258$ |
$0.524717144$ |
3.376245242 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 293 a - 292\) , \( -2018 a + 863\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(293a-292\right){x}-2018a+863$ |
| 36864.1-l7 |
36864.1-l |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{32} \cdot 3^{8} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.786181258$ |
$0.524717144$ |
3.376245242 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 773 a - 772\) , \( 9790 a - 5281\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(773a-772\right){x}+9790a-5281$ |
| 36864.1-l8 |
36864.1-l |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{34} \cdot 3^{10} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$5.572362516$ |
$0.262358572$ |
3.376245242 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4613 a - 4612\) , \( -137666 a + 66527\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(4613a-4612\right){x}-137666a+66527$ |
| 36864.1-m1 |
36864.1-m |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{28} \cdot 3^{7} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.393090629$ |
$1.049434289$ |
3.376245242 |
\( \frac{73696}{3} a - \frac{624368}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -67 a + 128\) , \( -346 a - 227\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-67a+128\right){x}-346a-227$ |
| 36864.1-m2 |
36864.1-m |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{28} \cdot 3^{7} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.348272657$ |
$1.049434289$ |
3.376245242 |
\( -\frac{73696}{3} a - \frac{550672}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -127 a + 68\) , \( -286 a + 445\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-127a+68\right){x}-286a+445$ |
| 36864.1-m3 |
36864.1-m |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{34} \cdot 3^{22} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.393090629$ |
$0.262358572$ |
3.376245242 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -187 a + 188\) , \( 8450 a - 4319\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-187a+188\right){x}+8450a-4319$ |
| 36864.1-m4 |
36864.1-m |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{8} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.696545314$ |
$2.098868579$ |
3.376245242 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -7 a + 8\) , \( -10 a + 1\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-7a+8\right){x}-10a+1$ |
| 36864.1-m5 |
36864.1-m |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{28} \cdot 3^{10} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.393090629$ |
$1.049434289$ |
3.376245242 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 53 a - 52\) , \( -142 a + 97\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(53a-52\right){x}-142a+97$ |
| 36864.1-m6 |
36864.1-m |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{32} \cdot 3^{14} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$2.786181258$ |
$0.524717144$ |
3.376245242 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 293 a - 292\) , \( 2018 a - 863\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(293a-292\right){x}+2018a-863$ |
| 36864.1-m7 |
36864.1-m |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{32} \cdot 3^{8} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.786181258$ |
$0.524717144$ |
3.376245242 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 773 a - 772\) , \( -9790 a + 5281\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(773a-772\right){x}-9790a+5281$ |
| 36864.1-m8 |
36864.1-m |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{34} \cdot 3^{10} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$5.572362516$ |
$0.262358572$ |
3.376245242 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 4613 a - 4612\) , \( 137666 a - 66527\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(4613a-4612\right){x}+137666a-66527$ |
| 36864.1-n1 |
36864.1-n |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{3} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cn[2] |
$1$ |
\( 2^{3} \) |
$0.285592593$ |
$2.612005765$ |
3.445485541 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a - 8\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(4a-8\right){x}$ |
| 36864.1-n2 |
36864.1-n |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{3} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cn[2] |
$1$ |
\( 2 \) |
$0.571185187$ |
$5.224011530$ |
3.445485541 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -a + 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a+2\right){x}$ |
*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.
