| 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 |
| 12288.1-a1 |
12288.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{30} \cdot 3^{8} \) |
$1.62956$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.337900933$ |
$1.172682149$ |
1.830202168 |
\( \frac{97336}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 31\) , \( 33\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+31{x}+33$ |
| 12288.1-a2 |
12288.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{24} \cdot 3^{4} \) |
$1.62956$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.675801867$ |
$2.345364298$ |
1.830202168 |
\( \frac{21952}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -9\) , \( 9\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-9{x}+9$ |
| 12288.1-a3 |
12288.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{12} \cdot 3^{2} \) |
$1.62956$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.337900933$ |
$4.690728597$ |
1.830202168 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -4\) , \( -2\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-4{x}-2$ |
| 12288.1-a4 |
12288.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{30} \cdot 3^{2} \) |
$1.62956$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.351603734$ |
$1.172682149$ |
1.830202168 |
\( \frac{7301384}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -129\) , \( 609\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-129{x}+609$ |
| 12288.1-b1 |
12288.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{28} \cdot 3 \) |
$1.62956$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.079273864$ |
$1.817673508$ |
2.265254003 |
\( \frac{73696}{3} a - \frac{624368}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -43 a + 20\) , \( 68 a - 103\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-43a+20\right){x}+68a-103$ |
| 12288.1-b2 |
12288.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{28} \cdot 3 \) |
$1.62956$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.079273864$ |
$1.817673508$ |
2.265254003 |
\( -\frac{73696}{3} a - \frac{550672}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -23 a - 20\) , \( -68 a - 35\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-23a-20\right){x}-68a-35$ |
| 12288.1-b3 |
12288.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{34} \cdot 3^{16} \) |
$1.62956$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.079273864$ |
$0.454418377$ |
2.265254003 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -63 a\) , \( 1377\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}-63a{x}+1377$ |
| 12288.1-b4 |
12288.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{20} \cdot 3^{2} \) |
$1.62956$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.539636932$ |
$3.635347017$ |
2.265254003 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -3 a\) , \( -3\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}-3a{x}-3$ |
| 12288.1-b5 |
12288.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{28} \cdot 3^{4} \) |
$1.62956$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.079273864$ |
$1.817673508$ |
2.265254003 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 17 a\) , \( -15\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+17a{x}-15$ |
| 12288.1-b6 |
12288.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{32} \cdot 3^{8} \) |
$1.62956$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$2.158547729$ |
$0.908836754$ |
2.265254003 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 97 a\) , \( 385\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+97a{x}+385$ |
| 12288.1-b7 |
12288.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{32} \cdot 3^{2} \) |
$1.62956$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.539636932$ |
$0.908836754$ |
2.265254003 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 257 a\) , \( -1503\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+257a{x}-1503$ |
| 12288.1-b8 |
12288.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{34} \cdot 3^{4} \) |
$1.62956$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$4.317095458$ |
$0.454418377$ |
2.265254003 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 1537 a\) , \( 23713\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+1537a{x}+23713$ |
| 12288.1-c1 |
12288.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{30} \cdot 3 \) |
$1.62956$ |
$(-2a+1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.438471408$ |
1.661003709 |
\( \frac{2285576}{3} a - \frac{71440}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -84 a + 43\) , \( -164 a + 253\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-84a+43\right){x}-164a+253$ |
| 12288.1-c2 |
12288.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{30} \cdot 3^{4} \) |
$1.62956$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.438471408$ |
1.661003709 |
\( -\frac{188632}{9} a - 7424 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -4 a + 43\) , \( -116 a + 29\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-4a+43\right){x}-116a+29$ |
| 12288.1-c3 |
12288.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{12} \cdot 3 \) |
$1.62956$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$5.753885633$ |
1.661003709 |
\( \frac{27712}{3} a - \frac{7040}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( a - 2\) , \( -a + 2\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(a-2\right){x}-a+2$ |
| 12288.1-c4 |
12288.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{24} \cdot 3^{2} \) |
$1.62956$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$2.876942816$ |
1.661003709 |
\( -\frac{1216}{3} a + \frac{64}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -4 a + 3\) , \( -4 a + 5\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-4a+3\right){x}-4a+5$ |
| 12288.1-d1 |
12288.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{30} \cdot 3^{4} \) |
$1.62956$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.438471408$ |
1.661003709 |
\( \frac{188632}{9} a - \frac{255448}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 4 a + 39\) , \( 116 a - 87\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(4a+39\right){x}+116a-87$ |
| 12288.1-d2 |
12288.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{24} \cdot 3^{2} \) |
$1.62956$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$2.876942816$ |
1.661003709 |
\( \frac{1216}{3} a - 384 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 4 a - 1\) , \( 4 a + 1\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(4a-1\right){x}+4a+1$ |
| 12288.1-d3 |
12288.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{12} \cdot 3 \) |
$1.62956$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$5.753885633$ |
1.661003709 |
\( -\frac{27712}{3} a + \frac{20672}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -a - 1\) , \( a + 1\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-a-1\right){x}+a+1$ |
| 12288.1-d4 |
12288.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{30} \cdot 3 \) |
$1.62956$ |
$(-2a+1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.438471408$ |
1.661003709 |
\( -\frac{2285576}{3} a + \frac{2214136}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 84 a - 41\) , \( 164 a + 89\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(84a-41\right){x}+164a+89$ |
| 12288.1-e1 |
12288.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{30} \cdot 3^{4} \) |
$1.62956$ |
$(-2a+1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.438471408$ |
1.661003709 |
\( \frac{188632}{9} a - \frac{255448}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -43 a + 4\) , \( -116 a + 87\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-43a+4\right){x}-116a+87$ |
| 12288.1-e2 |
12288.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{24} \cdot 3^{2} \) |
$1.62956$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$2.876942816$ |
1.661003709 |
\( \frac{1216}{3} a - 384 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -3 a + 4\) , \( -4 a - 1\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-3a+4\right){x}-4a-1$ |
| 12288.1-e3 |
12288.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{12} \cdot 3 \) |
$1.62956$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$5.753885633$ |
1.661003709 |
\( -\frac{27712}{3} a + \frac{20672}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 2 a - 1\) , \( -a - 1\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(2a-1\right){x}-a-1$ |
| 12288.1-e4 |
12288.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{30} \cdot 3 \) |
$1.62956$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.438471408$ |
1.661003709 |
\( -\frac{2285576}{3} a + \frac{2214136}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -43 a + 84\) , \( -164 a - 89\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-43a+84\right){x}-164a-89$ |
| 12288.1-f1 |
12288.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{30} \cdot 3 \) |
$1.62956$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.438471408$ |
1.661003709 |
\( \frac{2285576}{3} a - \frac{71440}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 41 a - 84\) , \( 164 a - 253\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(41a-84\right){x}+164a-253$ |
| 12288.1-f2 |
12288.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{30} \cdot 3^{4} \) |
$1.62956$ |
$(-2a+1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.438471408$ |
1.661003709 |
\( -\frac{188632}{9} a - 7424 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -39 a - 4\) , \( 116 a - 29\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-39a-4\right){x}+116a-29$ |
| 12288.1-f3 |
12288.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{12} \cdot 3 \) |
$1.62956$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$5.753885633$ |
1.661003709 |
\( \frac{27712}{3} a - \frac{7040}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( a + 1\) , \( a - 2\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(a+1\right){x}+a-2$ |
| 12288.1-f4 |
12288.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{24} \cdot 3^{2} \) |
$1.62956$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$2.876942816$ |
1.661003709 |
\( -\frac{1216}{3} a + \frac{64}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( a - 4\) , \( 4 a - 5\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(a-4\right){x}+4a-5$ |
| 12288.1-g1 |
12288.1-g |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{28} \cdot 3 \) |
$1.62956$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.817673508$ |
2.098868579 |
\( \frac{73696}{3} a - \frac{624368}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 20 a + 23\) , \( -68 a + 103\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(20a+23\right){x}-68a+103$ |
| 12288.1-g2 |
12288.1-g |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{28} \cdot 3 \) |
$1.62956$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.817673508$ |
2.098868579 |
\( -\frac{73696}{3} a - \frac{550672}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -20 a + 43\) , \( 68 a + 35\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-20a+43\right){x}+68a+35$ |
| 12288.1-g3 |
12288.1-g |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{34} \cdot 3^{16} \) |
$1.62956$ |
$(-2a+1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.454418377$ |
2.098868579 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 63\) , \( -1377\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+63{x}-1377$ |
| 12288.1-g4 |
12288.1-g |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{20} \cdot 3^{2} \) |
$1.62956$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$3.635347017$ |
2.098868579 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 3\) , \( 3\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+3{x}+3$ |
| 12288.1-g5 |
12288.1-g |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{28} \cdot 3^{4} \) |
$1.62956$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.817673508$ |
2.098868579 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -17\) , \( 15\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-17{x}+15$ |
| 12288.1-g6 |
12288.1-g |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{32} \cdot 3^{8} \) |
$1.62956$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.908836754$ |
2.098868579 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -97\) , \( -385\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-97{x}-385$ |
| 12288.1-g7 |
12288.1-g |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{32} \cdot 3^{2} \) |
$1.62956$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.908836754$ |
2.098868579 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -257\) , \( 1503\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-257{x}+1503$ |
| 12288.1-g8 |
12288.1-g |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{34} \cdot 3^{4} \) |
$1.62956$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.454418377$ |
2.098868579 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1537\) , \( -23713\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-1537{x}-23713$ |
| 12288.1-h1 |
12288.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{30} \cdot 3^{8} \) |
$1.62956$ |
$(-2a+1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.172682149$ |
2.708193418 |
\( \frac{97336}{81} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -31 a\) , \( -33\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}-31a{x}-33$ |
| 12288.1-h2 |
12288.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{24} \cdot 3^{4} \) |
$1.62956$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.345364298$ |
2.708193418 |
\( \frac{21952}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 9 a\) , \( -9\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+9a{x}-9$ |
| 12288.1-h3 |
12288.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{12} \cdot 3^{2} \) |
$1.62956$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4.690728597$ |
2.708193418 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 4 a\) , \( 2\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+4a{x}+2$ |
| 12288.1-h4 |
12288.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{30} \cdot 3^{2} \) |
$1.62956$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.172682149$ |
2.708193418 |
\( \frac{7301384}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 129 a\) , \( -609\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+129a{x}-609$ |
*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.
