| 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 |
| 129792.1-a1 |
129792.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{22} \cdot 3^{5} \cdot 13^{10} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$0.281315754$ |
0.649670905 |
\( -\frac{61226}{27} a + \frac{58564}{27} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -645 a + 590\) , \( -3361 a + 6855\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-645a+590\right){x}-3361a+6855$ |
| 129792.1-b1 |
129792.1-b |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{26} \cdot 3^{7} \cdot 13^{2} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$7$ |
7B |
$1$ |
\( 2 \) |
$1$ |
$0.913759368$ |
2.110236869 |
\( \frac{1853207}{81} a - \frac{1242731}{162} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 28 a - 108\) , \( -164 a + 404\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(28a-108\right){x}-164a+404$ |
| 129792.1-b2 |
129792.1-b |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{38} \cdot 3 \cdot 13^{2} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$7$ |
7B |
$1$ |
\( 2 \) |
$1$ |
$0.913759368$ |
2.110236869 |
\( -\frac{136583}{192} a + \frac{253379}{384} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 2 a - 43\) , \( -151 a + 170\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(2a-43\right){x}-151a+170$ |
| 129792.1-c1 |
129792.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{22} \cdot 3^{3} \cdot 13^{8} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$0.523136670$ |
1.208132389 |
\( -\frac{8878}{9} a + \frac{21986}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -179 a - 3\) , \( -615 a - 26\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-179a-3\right){x}-615a-26$ |
| 129792.1-d1 |
129792.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{16} \cdot 3 \cdot 13^{6} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$3.391541286$ |
$1.008263852$ |
3.948577566 |
\( \frac{73696}{3} a - \frac{624368}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 115 a + 10\) , \( 107 a - 577\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(115a+10\right){x}+107a-577$ |
| 129792.1-d2 |
129792.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{16} \cdot 3 \cdot 13^{6} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$3.391541286$ |
$1.008263852$ |
3.948577566 |
\( -\frac{73696}{3} a - \frac{550672}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 120\) , \( -548 a + 292\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+120{x}-548a+292$ |
| 129792.1-d3 |
129792.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{22} \cdot 3^{16} \cdot 13^{6} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.391541286$ |
$0.252065963$ |
3.948577566 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 110 a + 125\) , \( 6369 a + 2934\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(110a+125\right){x}+6369a+2934$ |
| 129792.1-d4 |
129792.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 13^{6} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.695770643$ |
$2.016527704$ |
3.948577566 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 5 a + 5\) , \( -6 a - 6\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(5a+5\right){x}-6a-6$ |
| 129792.1-d5 |
129792.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{16} \cdot 3^{4} \cdot 13^{6} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.847885321$ |
$1.008263852$ |
3.948577566 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -30 a - 35\) , \( -115 a - 34\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-30a-35\right){x}-115a-34$ |
| 129792.1-d6 |
129792.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{20} \cdot 3^{8} \cdot 13^{6} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.695770643$ |
$0.504131926$ |
3.948577566 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -170 a - 195\) , \( 1465 a + 806\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-170a-195\right){x}+1465a+806$ |
| 129792.1-d7 |
129792.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{20} \cdot 3^{2} \cdot 13^{6} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.423942660$ |
$0.504131926$ |
3.948577566 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -450 a - 515\) , \( -7471 a - 3226\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-450a-515\right){x}-7471a-3226$ |
| 129792.1-d8 |
129792.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{22} \cdot 3^{4} \cdot 13^{6} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.391541286$ |
$0.252065963$ |
3.948577566 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -2690 a - 3075\) , \( 102481 a + 50198\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-2690a-3075\right){x}+102481a+50198$ |
| 129792.1-e1 |
129792.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 13^{3} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.924294845$ |
$1.940723994$ |
4.142606386 |
\( -\frac{4479232}{27} a - 19968 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 27 a - 35\) , \( 88 a - 62\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(27a-35\right){x}+88a-62$ |
| 129792.1-e2 |
129792.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{16} \cdot 3^{12} \cdot 13^{3} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.848589691$ |
$0.970361997$ |
4.142606386 |
\( \frac{48688}{729} a + \frac{179408}{729} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 32 a - 20\) , \( 104 a - 144\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(32a-20\right){x}+104a-144$ |
| 129792.1-f1 |
129792.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 13^{9} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.538259990$ |
2.486116401 |
\( -\frac{4479232}{27} a - 19968 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -471 a + 306\) , \( -1962 a + 3915\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-471a+306\right){x}-1962a+3915$ |
| 129792.1-f2 |
129792.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{16} \cdot 3^{12} \cdot 13^{9} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.269129995$ |
2.486116401 |
\( \frac{48688}{729} a + \frac{179408}{729} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -386 a + 41\) , \( 57 a + 6150\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-386a+41\right){x}+57a+6150$ |
| 129792.1-g1 |
129792.1-g |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{22} \cdot 3^{5} \cdot 13^{4} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 3 \) |
$0.137483358$ |
$1.014298376$ |
3.864528128 |
\( -\frac{61226}{27} a + \frac{58564}{27} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -55 a + 26\) , \( 153 a - 114\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-55a+26\right){x}+153a-114$ |
| 129792.1-h1 |
129792.1-h |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{26} \cdot 3^{7} \cdot 13^{8} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$7$ |
7B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$0.253431250$ |
1.755823208 |
\( \frac{1853207}{81} a - \frac{1242731}{162} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -1055 a + 1394\) , \( -7247 a - 12434\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-1055a+1394\right){x}-7247a-12434$ |
| 129792.1-h2 |
129792.1-h |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{38} \cdot 3 \cdot 13^{8} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$7$ |
7B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$0.253431250$ |
1.755823208 |
\( -\frac{136583}{192} a + \frac{253379}{384} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -353 a + 627\) , \( 1255 a - 8053\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-353a+627\right){x}+1255a-8053$ |
| 129792.1-i1 |
129792.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{16} \cdot 3^{4} \cdot 13^{9} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.438213458$ |
$0.514251334$ |
4.083265571 |
\( -\frac{29104}{9} a - 3328 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 127 a - 266\) , \( 1215 a - 1725\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(127a-266\right){x}+1215a-1725$ |
| 129792.1-i2 |
129792.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 13^{9} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.719106729$ |
$1.028502668$ |
4.083265571 |
\( \frac{256}{3} a - \frac{4864}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 42 a - 1\) , \( 8 a - 159\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(42a-1\right){x}+8a-159$ |
| 129792.1-j1 |
129792.1-j |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{16} \cdot 3^{2} \cdot 13^{7} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.525231894$ |
2.425942203 |
\( \frac{178274368}{39} a - \frac{114526480}{13} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -579 a - 267\) , \( 8205 a - 762\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-579a-267\right){x}+8205a-762$ |
| 129792.1-j2 |
129792.1-j |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{16} \cdot 3^{8} \cdot 13^{7} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.525231894$ |
2.425942203 |
\( \frac{12519872}{1053} a - \frac{4457840}{351} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -304 a + 168\) , \( -1236 a + 1920\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-304a+168\right){x}-1236a+1920$ |
| 129792.1-j3 |
129792.1-j |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{16} \cdot 3^{2} \cdot 13^{10} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.525231894$ |
2.425942203 |
\( \frac{165562496}{85683} a - \frac{32807504}{28561} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 186 a - 117\) , \( 1155 a - 345\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(186a-117\right){x}+1155a-345$ |
| 129792.1-j4 |
129792.1-j |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 13^{8} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$1.050463788$ |
2.425942203 |
\( -\frac{4554752}{1521} a + \frac{2244608}{1521} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -39 a - 12\) , \( 126 a\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-39a-12\right){x}+126a$ |
| 129792.1-k1 |
129792.1-k |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{16} \cdot 3^{2} \cdot 13^{7} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.958508540$ |
$0.525231894$ |
4.650572641 |
\( \frac{178274368}{39} a - \frac{114526480}{13} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -579 a - 267\) , \( -8205 a + 762\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-579a-267\right){x}-8205a+762$ |
| 129792.1-k2 |
129792.1-k |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{16} \cdot 3^{8} \cdot 13^{7} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.958508540$ |
$0.525231894$ |
4.650572641 |
\( \frac{12519872}{1053} a - \frac{4457840}{351} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -304 a + 168\) , \( 1236 a - 1920\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-304a+168\right){x}+1236a-1920$ |
| 129792.1-k3 |
129792.1-k |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{16} \cdot 3^{2} \cdot 13^{10} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.958508540$ |
$0.525231894$ |
4.650572641 |
\( \frac{165562496}{85683} a - \frac{32807504}{28561} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 186 a - 117\) , \( -1155 a + 345\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(186a-117\right){x}-1155a+345$ |
| 129792.1-k4 |
129792.1-k |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 13^{8} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.917017080$ |
$1.050463788$ |
4.650572641 |
\( -\frac{4554752}{1521} a + \frac{2244608}{1521} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -39 a - 12\) , \( -126 a\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-39a-12\right){x}-126a$ |
| 129792.1-l1 |
129792.1-l |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{22} \cdot 3^{3} \cdot 13^{2} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 3 \) |
$0.081447333$ |
$1.886196087$ |
4.257398678 |
\( -\frac{8878}{9} a + \frac{21986}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -8 a + 16\) , \( -12\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-8a+16\right){x}-12$ |
| 129792.1-m1 |
129792.1-m |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{26} \cdot 3^{7} \cdot 13^{8} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$7$ |
7B |
$1$ |
\( 2^{2} \cdot 3 \cdot 7 \) |
$0.084177505$ |
$0.253431250$ |
4.138422892 |
\( \frac{1853207}{81} a - \frac{1242731}{162} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -339 a - 1055\) , \( 7247 a + 12434\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-339a-1055\right){x}+7247a+12434$ |
| 129792.1-m2 |
129792.1-m |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{38} \cdot 3 \cdot 13^{8} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$7$ |
7B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.589242537$ |
$0.253431250$ |
4.138422892 |
\( -\frac{136583}{192} a + \frac{253379}{384} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -274 a - 353\) , \( -1255 a + 8053\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-274a-353\right){x}-1255a+8053$ |
| 129792.1-n1 |
129792.1-n |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{22} \cdot 3^{5} \cdot 13^{4} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 3 \cdot 5 \) |
$0.038867494$ |
$1.014298376$ |
5.462643929 |
\( -\frac{61226}{27} a + \frac{58564}{27} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 26 a + 29\) , \( -153 a + 114\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(26a+29\right){x}-153a+114$ |
| 129792.1-o1 |
129792.1-o |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 13^{3} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.351001589$ |
$1.940723994$ |
4.719472685 |
\( -\frac{4479232}{27} a - 19968 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 27 a - 35\) , \( -88 a + 62\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(27a-35\right){x}-88a+62$ |
| 129792.1-o2 |
129792.1-o |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{16} \cdot 3^{12} \cdot 13^{3} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.175500794$ |
$0.970361997$ |
4.719472685 |
\( \frac{48688}{729} a + \frac{179408}{729} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 32 a - 20\) , \( -104 a + 144\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(32a-20\right){x}-104a+144$ |
| 129792.1-p1 |
129792.1-p |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 13^{9} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.538259990$ |
1.864587301 |
\( -\frac{4479232}{27} a - 19968 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 306 a + 165\) , \( 1962 a - 3915\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(306a+165\right){x}+1962a-3915$ |
| 129792.1-p2 |
129792.1-p |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{16} \cdot 3^{12} \cdot 13^{9} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.269129995$ |
1.864587301 |
\( \frac{48688}{729} a + \frac{179408}{729} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 41 a + 345\) , \( -57 a - 6150\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(41a+345\right){x}-57a-6150$ |
| 129792.1-q1 |
129792.1-q |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{22} \cdot 3 \cdot 13^{8} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$7.096426220$ |
$0.174282850$ |
5.712467020 |
\( -\frac{1028251680722}{507} a - \frac{94596173570}{507} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -14381 a + 6234\) , \( 488889 a - 581755\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-14381a+6234\right){x}+488889a-581755$ |
| 129792.1-q2 |
129792.1-q |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{16} \cdot 3^{4} \cdot 13^{8} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.774106555$ |
$0.697131401$ |
5.712467020 |
\( -\frac{52528}{1521} a + \frac{5072}{507} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -a - 26\) , \( 261 a - 451\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-a-26\right){x}+261a-451$ |
| 129792.1-q3 |
129792.1-q |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{22} \cdot 3 \cdot 13^{14} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$7.096426220$ |
$0.174282850$ |
5.712467020 |
\( \frac{2457991737026}{2447192163} a + \frac{3468181544930}{2447192163} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -1821 a + 1274\) , \( 537 a + 15509\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-1821a+1274\right){x}+537a+15509$ |
| 129792.1-q4 |
129792.1-q |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 13^{7} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.887053277$ |
$1.394262803$ |
5.712467020 |
\( \frac{539392}{39} a + \frac{478208}{39} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 34 a + 14\) , \( 33 a - 108\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(34a+14\right){x}+33a-108$ |
| 129792.1-q5 |
129792.1-q |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{20} \cdot 3^{2} \cdot 13^{10} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$3.548213110$ |
$0.348565700$ |
5.712467020 |
\( -\frac{4035638236}{85683} a + \frac{3926320864}{85683} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -901 a + 394\) , \( 7785 a - 9235\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-901a+394\right){x}+7785a-9235$ |
| 129792.1-q6 |
129792.1-q |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{20} \cdot 3^{8} \cdot 13^{7} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$0.887053277$ |
$0.348565700$ |
5.712467020 |
\( \frac{89672548}{1053} a + \frac{92596592}{1053} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 339 a - 1086\) , \( 6129 a - 13059\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(339a-1086\right){x}+6129a-13059$ |
| 129792.1-r1 |
129792.1-r |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{26} \cdot 3^{7} \cdot 13^{2} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$7$ |
7B |
$1$ |
\( 2^{2} \cdot 7 \) |
$0.095573825$ |
$0.913759368$ |
5.647135503 |
\( \frac{1853207}{81} a - \frac{1242731}{162} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 80 a + 28\) , \( 164 a - 404\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(80a+28\right){x}+164a-404$ |
| 129792.1-r2 |
129792.1-r |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{38} \cdot 3 \cdot 13^{2} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$7$ |
7B |
$1$ |
\( 2^{2} \) |
$0.669016780$ |
$0.913759368$ |
5.647135503 |
\( -\frac{136583}{192} a + \frac{253379}{384} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 41 a + 2\) , \( 151 a - 170\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(41a+2\right){x}+151a-170$ |
| 129792.1-s1 |
129792.1-s |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{22} \cdot 3^{5} \cdot 13^{10} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$0.281315754$ |
3.248354528 |
\( -\frac{61226}{27} a + \frac{58564}{27} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 55 a - 645\) , \( 3361 a - 6855\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(55a-645\right){x}+3361a-6855$ |
| 129792.1-t1 |
129792.1-t |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{16} \cdot 3^{4} \cdot 13^{3} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.854159553$ |
4.281998069 |
\( -\frac{29104}{9} a - 3328 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 17 a - 18\) , \( 43 a - 26\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(17a-18\right){x}+43a-26$ |
| 129792.1-t2 |
129792.1-t |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
129792.1 |
\( 2^{8} \cdot 3 \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 13^{3} \) |
$2.93773$ |
$(-2a+1), (-4a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.708319106$ |
4.281998069 |
\( \frac{256}{3} a - \frac{4864}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 2 a + 2\) , \( 3 a - 3\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(2a+2\right){x}+3a-3$ |
*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.
