| 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 |
| 768.1-a1 |
768.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( - 2^{12} \cdot 3 \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$26.09005771$ |
1.882887730 |
\( -\frac{166016}{3} a + 95936 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 1354602 a - 2346237\) , \( -1124664415 a + 1947975909\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(1354602a-2346237\right){x}-1124664415a+1947975909$ |
| 768.1-a2 |
768.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( - 2^{21} \cdot 3^{2} \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.630628607$ |
1.882887730 |
\( -\frac{164847992914}{3} a + \frac{285525100658}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 36546 a - 63297\) , \( 4995933 a - 8653209\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(36546a-63297\right){x}+4995933a-8653209$ |
| 768.1-a3 |
768.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{18} \cdot 3^{4} \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$6.522514429$ |
1.882887730 |
\( -\frac{1122088}{9} a + \frac{1989808}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2286 a - 3957\) , \( 77553 a - 134325\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(2286a-3957\right){x}+77553a-134325$ |
| 768.1-a4 |
768.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{12} \cdot 3^{2} \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$26.09005771$ |
1.882887730 |
\( \frac{9856}{3} a + \frac{22336}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 37894 a - 65634\) , \( 667716 a - 1156518\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(37894a-65634\right){x}+667716a-1156518$ |
| 768.1-a5 |
768.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( - 2^{21} \cdot 3^{8} \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.630628607$ |
1.882887730 |
\( \frac{443186854}{81} a + \frac{767608522}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -10 a - 41\) , \( 11 a - 177\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-10a-41\right){x}+11a-177$ |
| 768.1-a6 |
768.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( - 2^{18} \cdot 3 \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$13.04502885$ |
1.882887730 |
\( \frac{132636728}{3} a + 76579552 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -150276 a + 260286\) , \( 5169562 a - 8953944\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-150276a+260286\right){x}+5169562a-8953944$ |
| 768.1-b1 |
768.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( - 2^{19} \cdot 3^{12} \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.067825433$ |
1.174280054 |
\( -\frac{217996}{729} a + \frac{1023628}{729} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 942 a - 1629\) , \( -6345 a + 10989\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(942a-1629\right){x}-6345a+10989$ |
| 768.1-b2 |
768.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{14} \cdot 3^{6} \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$8.135650867$ |
1.174280054 |
\( -\frac{770336}{27} a + \frac{1419904}{27} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 532 a - 919\) , \( 8829 a - 15293\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(532a-919\right){x}+8829a-15293$ |
| 768.1-b3 |
768.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{19} \cdot 3^{3} \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.067825433$ |
1.174280054 |
\( -\frac{26639622068}{9} a + \frac{15380474156}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 8482 a - 14689\) , \( 561627 a - 972767\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(8482a-14689\right){x}+561627a-972767$ |
| 768.1-b4 |
768.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( - 2^{16} \cdot 3^{3} \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.067825433$ |
1.174280054 |
\( \frac{14225792}{9} a + \frac{8213248}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 2 a - 5\) , \( 50 a - 87\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(2a-5\right){x}+50a-87$ |
| 768.1-c1 |
768.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( - 2^{21} \cdot 3^{8} \) |
$1.62956$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.211834002$ |
$8.988372149$ |
2.198599305 |
\( -\frac{443186854}{81} a + \frac{767608522}{81} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 10 a - 41\) , \( 11 a + 177\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(10a-41\right){x}+11a+177$ |
| 768.1-c2 |
768.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( - 2^{18} \cdot 3 \) |
$1.62956$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.694672022$ |
$4.494186074$ |
2.198599305 |
\( -\frac{132636728}{3} a + 76579552 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 200974 a - 348097\) , \( 64360541 a - 111475727\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(200974a-348097\right){x}+64360541a-111475727$ |
| 768.1-c3 |
768.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{12} \cdot 3^{2} \) |
$1.62956$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.847336011$ |
$17.97674429$ |
2.198599305 |
\( -\frac{9856}{3} a + \frac{22336}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 12804 a - 22177\) , \( 955655 a - 1655243\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(12804a-22177\right){x}+955655a-1655243$ |
| 768.1-c4 |
768.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( - 2^{12} \cdot 3 \) |
$1.62956$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.694672022$ |
$8.988372149$ |
2.198599305 |
\( \frac{166016}{3} a + 95936 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -43196 a + 74818\) , \( 28011318 a - 48517026\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-43196a+74818\right){x}+28011318a-48517026$ |
| 768.1-c5 |
768.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{18} \cdot 3^{4} \) |
$1.62956$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.423668005$ |
$17.97674429$ |
2.198599305 |
\( \frac{1122088}{9} a + \frac{1989808}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 216 a - 374\) , \( -1926 a + 3336\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(216a-374\right){x}-1926a+3336$ |
| 768.1-c6 |
768.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( - 2^{21} \cdot 3^{2} \) |
$1.62956$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.211834002$ |
$8.988372149$ |
2.198599305 |
\( \frac{164847992914}{3} a + \frac{285525100658}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -444 a + 766\) , \( -10806 a + 18720\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-444a+766\right){x}-10806a+18720$ |
| 768.1-d1 |
768.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( - 2^{19} \cdot 3^{4} \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.670482934$ |
2.119154310 |
\( -\frac{2695276}{3} a + \frac{14006500}{9} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 32 a - 54\) , \( 138 a - 240\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(32a-54\right){x}+138a-240$ |
| 768.1-d2 |
768.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( - 2^{16} \cdot 3 \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$14.68193173$ |
2.119154310 |
\( \frac{4736}{3} a + 3840 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -24 a + 44\) , \( 72 a - 124\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-24a+44\right){x}+72a-124$ |
| 768.1-d3 |
768.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{14} \cdot 3^{2} \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$14.68193173$ |
2.119154310 |
\( 2080 a + \frac{18688}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 2 a - 4\) , \( 2 a - 4\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(2a-4\right){x}+2a-4$ |
| 768.1-d4 |
768.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{19} \cdot 3 \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.340965868$ |
2.119154310 |
\( \frac{71147500}{3} a + 41116428 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 12 a - 34\) , \( -46 a + 56\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(12a-34\right){x}-46a+56$ |
| 768.1-e1 |
768.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( - 2^{22} \cdot 3 \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$0.710438564$ |
1.640687586 |
\( -\frac{79558124472974}{3} a + 45932904578280 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 4138 a - 7169\) , \( 191739 a - 332103\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(4138a-7169\right){x}+191739a-332103$ |
| 768.1-e2 |
768.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{22} \cdot 3^{16} \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.841754258$ |
1.640687586 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 62 a + 111\) , \( 2637 a + 4569\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(62a+111\right){x}+2637a+4569$ |
| 768.1-e3 |
768.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$11.36701703$ |
1.640687586 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -520 a + 901\) , \( 10685 a - 18507\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-520a+901\right){x}+10685a-18507$ |
| 768.1-e4 |
768.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{16} \cdot 3^{4} \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$11.36701703$ |
1.640687586 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 18 a - 29\) , \( 43 a - 75\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(18a-29\right){x}+43a-75$ |
| 768.1-e5 |
768.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{20} \cdot 3^{8} \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$11.36701703$ |
1.640687586 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -98 a - 169\) , \( 637 a + 1105\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-98a-169\right){x}+637a+1105$ |
| 768.1-e6 |
768.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{20} \cdot 3^{2} \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$2.841754258$ |
1.640687586 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 258 a - 449\) , \( 3043 a - 5271\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(258a-449\right){x}+3043a-5271$ |
| 768.1-e7 |
768.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{22} \cdot 3^{4} \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$11.36701703$ |
1.640687586 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -1538 a - 2689\) , \( 43117 a + 74761\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-1538a-2689\right){x}+43117a+74761$ |
| 768.1-e8 |
768.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( - 2^{22} \cdot 3 \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$0.710438564$ |
1.640687586 |
\( \frac{79558124472974}{3} a + 45932904578280 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 218 a - 449\) , \( 3467 a - 6183\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(218a-449\right){x}+3467a-6183$ |
| 768.1-f1 |
768.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( - 2^{16} \cdot 3^{3} \) |
$1.62956$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.089484422$ |
$18.42598142$ |
2.855871714 |
\( -\frac{14225792}{9} a + \frac{8213248}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -2 a - 5\) , \( 50 a + 87\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-2a-5\right){x}+50a+87$ |
| 768.1-f2 |
768.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( - 2^{19} \cdot 3^{12} \) |
$1.62956$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.089484422$ |
$4.606495355$ |
2.855871714 |
\( \frac{217996}{729} a + \frac{1023628}{729} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -10 a + 3\) , \( -15 a + 3\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-10a+3\right){x}-15a+3$ |
| 768.1-f3 |
768.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{14} \cdot 3^{6} \) |
$1.62956$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.178968844$ |
$18.42598142$ |
2.855871714 |
\( \frac{770336}{27} a + \frac{1419904}{27} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -7\) , \( -a + 5\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-7{x}-a+5$ |
| 768.1-f4 |
768.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{19} \cdot 3^{3} \) |
$1.62956$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.357937689$ |
$9.212990711$ |
2.855871714 |
\( \frac{26639622068}{9} a + \frac{15380474156}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -30 a - 97\) , \( 197 a + 239\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-30a-97\right){x}+197a+239$ |
| 768.1-g1 |
768.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( - 2^{18} \cdot 3 \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$16.03449474$ |
2.314379964 |
\( -\frac{1842168016}{3} a + 1063576200 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 20 a - 34\) , \( -54 a + 104\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(20a-34\right){x}-54a+104$ |
| 768.1-g2 |
768.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{18} \cdot 3^{8} \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$4.008623686$ |
2.314379964 |
\( \frac{97336}{81} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -5980 a + 10358\) , \( 217250 a - 376288\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-5980a+10358\right){x}+217250a-376288$ |
| 768.1-g3 |
768.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{12} \cdot 3^{4} \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$16.03449474$ |
2.314379964 |
\( \frac{21952}{9} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 1820 a - 3152\) , \( 30640 a - 53070\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(1820a-3152\right){x}+30640a-53070$ |
| 768.1-g4 |
768.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{12} \cdot 3^{2} \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$32.06898949$ |
2.314379964 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 242 a - 419\) , \( -2437 a + 4221\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(242a-419\right){x}-2437a+4221$ |
| 768.1-g5 |
768.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{18} \cdot 3^{2} \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.008623686$ |
2.314379964 |
\( \frac{7301384}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 25220 a - 43682\) , \( 2876590 a - 4982400\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(25220a-43682\right){x}+2876590a-4982400$ |
| 768.1-g6 |
768.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( - 2^{18} \cdot 3 \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$16.03449474$ |
2.314379964 |
\( \frac{1842168016}{3} a + 1063576200 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -18 a + 31\) , \( -8073 a + 13983\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-18a+31\right){x}-8073a+13983$ |
| 768.1-h1 |
768.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( - 2^{16} \cdot 3 \) |
$1.62956$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.595402747$ |
$12.66634840$ |
2.177066230 |
\( -\frac{4736}{3} a + 3840 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 4 a - 4\) , \( 4 a - 8\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(4a-4\right){x}+4a-8$ |
| 768.1-h2 |
768.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{14} \cdot 3^{2} \) |
$1.62956$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.297701373$ |
$25.33269681$ |
2.177066230 |
\( -2080 a + \frac{18688}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -2 a - 4\) , \( 2 a + 4\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-2a-4\right){x}+2a+4$ |
| 768.1-h3 |
768.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{19} \cdot 3 \) |
$1.62956$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.595402747$ |
$12.66634840$ |
2.177066230 |
\( -\frac{71147500}{3} a + 41116428 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -12 a - 34\) , \( -46 a - 56\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-12a-34\right){x}-46a-56$ |
| 768.1-h4 |
768.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( - 2^{19} \cdot 3^{4} \) |
$1.62956$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.148850686$ |
$12.66634840$ |
2.177066230 |
\( \frac{2695276}{3} a + \frac{14006500}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -32 a - 54\) , \( 138 a + 240\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-32a-54\right){x}+138a+240$ |
| 768.1-i1 |
768.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( - 2^{16} \cdot 3 \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$14.68193173$ |
2.119154310 |
\( -\frac{4736}{3} a + 3840 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4 a - 4\) , \( -4 a + 8\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(4a-4\right){x}-4a+8$ |
| 768.1-i2 |
768.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{14} \cdot 3^{2} \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$14.68193173$ |
2.119154310 |
\( -2080 a + \frac{18688}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -2 a - 4\) , \( -2 a - 4\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-2a-4\right){x}-2a-4$ |
| 768.1-i3 |
768.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{19} \cdot 3 \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.340965868$ |
2.119154310 |
\( -\frac{71147500}{3} a + 41116428 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -12 a - 34\) , \( 46 a + 56\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-12a-34\right){x}+46a+56$ |
| 768.1-i4 |
768.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( - 2^{19} \cdot 3^{4} \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.670482934$ |
2.119154310 |
\( \frac{2695276}{3} a + \frac{14006500}{9} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -32 a - 54\) , \( -138 a - 240\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-32a-54\right){x}-138a-240$ |
| 768.1-j1 |
768.1-j |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( - 2^{18} \cdot 3 \) |
$1.62956$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.703207468$ |
$2.744450027$ |
2.141628230 |
\( -\frac{1842168016}{3} a + 1063576200 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 20 a - 34\) , \( 54 a - 104\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(20a-34\right){x}+54a-104$ |
| 768.1-j2 |
768.1-j |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{18} \cdot 3^{8} \) |
$1.62956$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.337900933$ |
$5.488900054$ |
2.141628230 |
\( \frac{97336}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -5980 a + 10358\) , \( -217250 a + 376288\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-5980a+10358\right){x}-217250a+376288$ |
| 768.1-j3 |
768.1-j |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{12} \cdot 3^{4} \) |
$1.62956$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.675801867$ |
$21.95560021$ |
2.141628230 |
\( \frac{21952}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 1820 a - 3152\) , \( -30640 a + 53070\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(1820a-3152\right){x}-30640a+53070$ |
| 768.1-j4 |
768.1-j |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{12} \cdot 3^{2} \) |
$1.62956$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1.351603734$ |
$10.97780010$ |
2.141628230 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 242 a - 419\) , \( 2437 a - 4221\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(242a-419\right){x}+2437a-4221$ |
*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.
