| 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 |
| 96.4-a1 |
96.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( - 2^{32} \cdot 3^{7} \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 7 \) |
$1$ |
$0.802508557$ |
1.488127972 |
\( -\frac{449724950229373}{5308416} a + \frac{1922536988893439}{5308416} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 4615 a + 15115\) , \( -4216389 a - 13808325\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(4615a+15115\right){x}-4216389a-13808325$ |
| 96.4-a2 |
96.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( 2^{20} \cdot 3^{28} \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 7 \) |
$1$ |
$1.605017115$ |
1.488127972 |
\( \frac{248028267187}{76527504} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -133 a - 657\) , \( 1256 a + 4664\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-133a-657\right){x}+1256a+4664$ |
| 96.4-a3 |
96.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( 2^{28} \cdot 3^{14} \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \cdot 7 \) |
$1$ |
$1.605017115$ |
1.488127972 |
\( \frac{14580432307}{559872} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -53 a - 257\) , \( -504 a - 2088\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-53a-257\right){x}-504a-2088$ |
| 96.4-a4 |
96.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( - 2^{32} \cdot 3^{7} \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 7 \) |
$1$ |
$0.802508557$ |
1.488127972 |
\( \frac{449724950229373}{5308416} a + \frac{736406019332033}{2654208} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -854 a + 3683\) , \( 340051 a - 1453661\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-854a+3683\right){x}+340051a-1453661$ |
| 96.4-b1 |
96.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( - 2^{14} \cdot 3^{3} \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.871346892$ |
$16.36852408$ |
3.778271621 |
\( -\frac{351013}{144} a + \frac{1701239}{144} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 17 a - 82\) , \( -51 a + 213\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(17a-82\right){x}-51a+213$ |
| 96.4-b2 |
96.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( 2^{10} \cdot 3^{6} \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.742693784$ |
$16.36852408$ |
3.778271621 |
\( -\frac{24335}{108} a + \frac{333893}{108} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 9508 a - 40648\) , \( 727273 a - 3109031\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(9508a-40648\right){x}+727273a-3109031$ |
| 96.4-b3 |
96.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( - 2^{11} \cdot 3^{12} \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.485387569$ |
$4.092131021$ |
3.778271621 |
\( \frac{13159651}{1458} a + \frac{4901983}{162} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -23702 a + 101322\) , \( 4672577 a - 19974879\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-23702a+101322\right){x}+4672577a-19974879$ |
| 96.4-b4 |
96.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( 2^{5} \cdot 3^{3} \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$3.485387569$ |
$16.36852408$ |
3.778271621 |
\( -\frac{18247675}{18} a + \frac{104191529}{18} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -581 a - 1895\) , \( 14004 a + 45867\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-581a-1895\right){x}+14004a+45867$ |
| 96.4-c1 |
96.4-c |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( - 2^{20} \cdot 3 \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$13.51429459$ |
3.580024093 |
\( -\frac{152551}{768} a + \frac{1106381}{768} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 41 a + 142\) , \( 469 a + 1541\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(41a+142\right){x}+469a+1541$ |
| 96.4-c2 |
96.4-c |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$13.51429459$ |
3.580024093 |
\( -\frac{436639}{48} a + \frac{691831}{16} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 4 a - 20\) , \( 9 a - 39\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(4a-20\right){x}+9a-39$ |
| 96.4-c3 |
96.4-c |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( 2^{14} \cdot 3^{4} \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$3.378573647$ |
3.580024093 |
\( -\frac{24913903427}{36} a + \frac{106505465453}{36} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 64 a - 280\) , \( 553 a - 2375\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(64a-280\right){x}+553a-2375$ |
| 96.4-c4 |
96.4-c |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( - 2^{14} \cdot 3 \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$13.51429459$ |
3.580024093 |
\( \frac{20041777}{12} a + \frac{65635153}{12} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 102 a - 394\) , \( 52512 a - 224432\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(102a-394\right){x}+52512a-224432$ |
| 96.4-d1 |
96.4-d |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( - 2^{8} \cdot 3 \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$18.75454831$ |
2.484100608 |
\( -\frac{31759}{48} a + \frac{135557}{48} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 749 a - 3204\) , \( -17453 a + 74611\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(749a-3204\right){x}-17453a+74611$ |
| 96.4-d2 |
96.4-d |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( 2^{10} \cdot 3^{2} \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$18.75454831$ |
2.484100608 |
\( -\frac{9289735}{4} a + \frac{120300487}{12} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 11334 a - 48454\) , \( -1274937 a + 5450251\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(11334a-48454\right){x}-1274937a+5450251$ |
| 96.4-e1 |
96.4-e |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( 2^{19} \cdot 3 \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.826928706$ |
$6.217324322$ |
3.008968840 |
\( -\frac{163415}{768} a + \frac{589213}{768} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -16 a - 48\) , \( -212 a - 692\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-16a-48\right){x}-212a-692$ |
| 96.4-e2 |
96.4-e |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( - 2^{11} \cdot 3^{2} \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.913464353$ |
$12.43464864$ |
3.008968840 |
\( -\frac{370613256209}{2} a + \frac{4753022980441}{6} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 106276 a - 454300\) , \( -36558610 a + 156285050\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(106276a-454300\right){x}-36558610a+156285050$ |
| 96.4-e3 |
96.4-e |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( 2^{10} \cdot 3^{4} \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.456732176$ |
$24.86929729$ |
3.008968840 |
\( -\frac{1878415}{12} a + \frac{24152911}{36} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 6646 a - 28390\) , \( -567172 a + 2424632\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(6646a-28390\right){x}-567172a+2424632$ |
| 96.4-e4 |
96.4-e |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( - 2^{5} \cdot 3^{8} \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.228366088$ |
$24.86929729$ |
3.008968840 |
\( \frac{1539923}{54} a + \frac{15047213}{162} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -1975 a - 6465\) , \( 86004 a + 281655\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-1975a-6465\right){x}+86004a+281655$ |
| 96.4-e5 |
96.4-e |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( 2^{14} \cdot 3^{2} \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.913464353$ |
$12.43464864$ |
3.008968840 |
\( \frac{817075}{16} a + \frac{8125069}{48} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 7 a + 4\) , \( 36\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(7a+4\right){x}+36$ |
| 96.4-e6 |
96.4-e |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( 2^{13} \cdot 3 \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.826928706$ |
$3.108662161$ |
3.008968840 |
\( \frac{237846527975}{12} a + \frac{778928661611}{12} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 27 a - 96\) , \( 100 a - 464\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(27a-96\right){x}+100a-464$ |
| 96.4-f1 |
96.4-f |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( - 2^{6} \cdot 3^{5} \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$14.56141634$ |
4.821766779 |
\( -\frac{23623}{108} a + \frac{111341}{108} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 6 a + 20\) , \( -10 a - 35\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(6a+20\right){x}-10a-35$ |
| 96.4-f2 |
96.4-f |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( - 2^{9} \cdot 3^{10} \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$7.280708174$ |
4.821766779 |
\( \frac{698507}{486} a + \frac{3118087}{486} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -49 a - 160\) , \( -537 a - 1761\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-49a-160\right){x}-537a-1761$ |
| 96.4-g1 |
96.4-g |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( - 2^{8} \cdot 3 \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$25.79187584$ |
1.708108705 |
\( -\frac{31759}{48} a + \frac{135557}{48} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 4 a + 16\) , \( 7 a + 22\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(4a+16\right){x}+7a+22$ |
| 96.4-g2 |
96.4-g |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( 2^{10} \cdot 3^{2} \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$12.89593792$ |
1.708108705 |
\( -\frac{9289735}{4} a + \frac{120300487}{12} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -11 a - 34\) , \( 16 a + 52\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-11a-34\right){x}+16a+52$ |
| 96.4-h1 |
96.4-h |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( 2^{19} \cdot 3 \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.702891533$ |
$11.44078906$ |
4.260561653 |
\( -\frac{163415}{768} a + \frac{589213}{768} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -347 a + 1474\) , \( 2233 a - 9551\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-347a+1474\right){x}+2233a-9551$ |
| 96.4-h2 |
96.4-h |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( - 2^{11} \cdot 3^{2} \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$5.623132268$ |
$2.860197265$ |
4.260561653 |
\( -\frac{370613256209}{2} a + \frac{4753022980441}{6} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 22 a + 71\) , \( 41 a + 113\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(22a+71\right){x}+41a+113$ |
| 96.4-h3 |
96.4-h |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( 2^{10} \cdot 3^{4} \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$2.811566134$ |
$11.44078906$ |
4.260561653 |
\( -\frac{1878415}{12} a + \frac{24152911}{36} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -8 a - 19\) , \( -7 a - 19\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-8a-19\right){x}-7a-19$ |
| 96.4-h4 |
96.4-h |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( - 2^{5} \cdot 3^{8} \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$5.623132268$ |
$5.720394531$ |
4.260561653 |
\( \frac{1539923}{54} a + \frac{15047213}{162} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 10 a - 45\) , \( 71 a - 303\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(10a-45\right){x}+71a-303$ |
| 96.4-h5 |
96.4-h |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( 2^{14} \cdot 3^{2} \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.405783067$ |
$22.88157812$ |
4.260561653 |
\( \frac{817075}{16} a + \frac{8125069}{48} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -11681 a - 38253\) , \( 1289371 a + 4222583\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-11681a-38253\right){x}+1289371a+4222583$ |
| 96.4-h6 |
96.4-h |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( 2^{13} \cdot 3 \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.811566134$ |
$22.88157812$ |
4.260561653 |
\( \frac{237846527975}{12} a + \frac{778928661611}{12} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -186861 a - 611953\) , \( 84731071 a + 277487243\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-186861a-611953\right){x}+84731071a+277487243$ |
| 96.4-i1 |
96.4-i |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( - 2^{6} \cdot 3^{5} \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$21.13304394$ |
1.399570025 |
\( -\frac{23623}{108} a + \frac{111341}{108} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 294 a - 1245\) , \( 585 a - 2493\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(294a-1245\right){x}+585a-2493$ |
| 96.4-i2 |
96.4-i |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( - 2^{9} \cdot 3^{10} \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$10.56652197$ |
1.399570025 |
\( \frac{698507}{486} a + \frac{3118087}{486} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -1161 a + 4975\) , \( 4317 a - 18447\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-1161a+4975\right){x}+4317a-18447$ |
| 96.4-j1 |
96.4-j |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( - 2^{14} \cdot 3^{3} \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.179115172$ |
$9.242546028$ |
2.631284547 |
\( -\frac{351013}{144} a + \frac{1701239}{144} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 828 a + 2716\) , \( -11648 a - 38144\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(828a+2716\right){x}-11648a-38144$ |
| 96.4-j2 |
96.4-j |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( 2^{10} \cdot 3^{6} \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.358230344$ |
$18.48509205$ |
2.631284547 |
\( -\frac{24335}{108} a + \frac{333893}{108} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 3 a + 12\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(3a+12\right){x}$ |
| 96.4-j3 |
96.4-j |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( - 2^{11} \cdot 3^{12} \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.179115172$ |
$9.242546028$ |
2.631284547 |
\( \frac{13159651}{1458} a + \frac{4901983}{162} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -7 a - 18\) , \( 6 a + 18\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-7a-18\right){x}+6a+18$ |
| 96.4-j4 |
96.4-j |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( 2^{5} \cdot 3^{3} \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.716460688$ |
$18.48509205$ |
2.631284547 |
\( -\frac{18247675}{18} a + \frac{104191529}{18} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 273 a - 1146\) , \( -4494 a + 19230\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(273a-1146\right){x}-4494a+19230$ |
| 96.4-k1 |
96.4-k |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( - 2^{20} \cdot 3 \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$9.247932164$ |
2.449837077 |
\( -\frac{152551}{768} a + \frac{1106381}{768} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 255 a - 1069\) , \( 1963 a - 8373\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(255a-1069\right){x}+1963a-8373$ |
| 96.4-k2 |
96.4-k |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$18.49586432$ |
2.449837077 |
\( -\frac{436639}{48} a + \frac{691831}{16} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -9821 a - 32160\) , \( -833280 a - 2728924\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-9821a-32160\right){x}-833280a-2728924$ |
| 96.4-k3 |
96.4-k |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( 2^{14} \cdot 3^{4} \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$18.49586432$ |
2.449837077 |
\( -\frac{24913903427}{36} a + \frac{106505465453}{36} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -52161 a - 170820\) , \( 11740716 a + 38449872\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-52161a-170820\right){x}+11740716a+38449872$ |
| 96.4-k4 |
96.4-k |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( - 2^{14} \cdot 3 \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$9.247932164$ |
2.449837077 |
\( \frac{20041777}{12} a + \frac{65635153}{12} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -50 a - 162\) , \( -540 a - 1768\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-50a-162\right){x}-540a-1768$ |
| 96.4-l1 |
96.4-l |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( - 2^{32} \cdot 3^{7} \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$4.178695124$ |
2.213926761 |
\( -\frac{449724950229373}{5308416} a + \frac{1922536988893439}{5308416} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 6007 a - 25637\) , \( -495669 a + 2118999\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(6007a-25637\right){x}-495669a+2118999$ |
| 96.4-l2 |
96.4-l |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( 2^{20} \cdot 3^{28} \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$1.044673781$ |
2.213926761 |
\( \frac{248028267187}{76527504} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 2727736 a - 11660855\) , \( 3260456517 a - 13938181707\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2727736a-11660855\right){x}+3260456517a-13938181707$ |
| 96.4-l3 |
96.4-l |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( 2^{28} \cdot 3^{14} \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$4.178695124$ |
2.213926761 |
\( \frac{14580432307}{559872} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 1060616 a - 4534055\) , \( -1114243483 a + 4763298645\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(1060616a-4534055\right){x}-1114243483a+4763298645$ |
| 96.4-l4 |
96.4-l |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
96.4 |
\( 2^{5} \cdot 3 \) |
\( - 2^{32} \cdot 3^{7} \) |
$2.11176$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$4.178695124$ |
2.213926761 |
\( \frac{449724950229373}{5308416} a + \frac{736406019332033}{2654208} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -32262 a - 105654\) , \( 6009228 a + 19679724\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-32262a-105654\right){x}+6009228a+19679724$ |
*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.
