| 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 |
| 128.5-a1 |
128.5-a |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( - 2^{33} \) |
$2.26923$ |
$(a-4), (a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{4} \cdot 3 \) |
$1.308640542$ |
$4.933598406$ |
5.130952434 |
\( -\frac{1536003}{4096} a + \frac{3288897}{2048} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 116 a + 396\) , \( -33568 a - 109920\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(116a+396\right){x}-33568a-109920$ |
| 128.5-a2 |
128.5-a |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( - 2^{33} \) |
$2.26923$ |
$(a-4), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{2} \cdot 3 \) |
$1.308640542$ |
$4.933598406$ |
5.130952434 |
\( \frac{1536003}{4096} a + \frac{5041791}{4096} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -7 a + 30\) , \( 269 a - 1150\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-7a+30\right){x}+269a-1150$ |
| 128.5-a3 |
128.5-a |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{30} \) |
$2.26923$ |
$(a-4), (a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3Ns |
$1$ |
\( 2^{3} \cdot 3 \) |
$2.617281085$ |
$4.933598406$ |
5.130952434 |
\( \frac{2146689}{64} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 52767 a - 225574\) , \( 12607701 a - 53896878\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(52767a-225574\right){x}+12607701a-53896878$ |
| 128.5-a4 |
128.5-a |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{24} \) |
$2.26923$ |
$(a-4), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{2} \cdot 3 \) |
$5.234562170$ |
$1.233399601$ |
5.130952434 |
\( \frac{8602523649}{8} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 838167 a - 3583094\) , \( 813490941 a - 3477606430\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(838167a-3583094\right){x}+813490941a-3477606430$ |
| 128.5-b1 |
128.5-b |
$1$ |
$1$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{20} \) |
$2.26923$ |
$(a-4), (a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.098910500$ |
$22.23091247$ |
2.329980302 |
\( -\frac{25991}{32} a - \frac{85779}{16} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -2 a + 3\) , \( 5\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-2a+3\right){x}+5$ |
| 128.5-c1 |
128.5-c |
$4$ |
$21$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{22} \) |
$2.26923$ |
$(a-4), (a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 7$ |
3B, 7B.6.3 |
$49$ |
\( 2 \) |
$1$ |
$0.473006225$ |
6.139818101 |
\( -\frac{293180476215589246298781}{8} a - \frac{960141789432972248487021}{8} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 115785 a - 497049\) , \( 41797219 a - 178648906\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(115785a-497049\right){x}+41797219a-178648906$ |
| 128.5-c2 |
128.5-c |
$4$ |
$21$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{22} \) |
$2.26923$ |
$(a-4), (a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 7$ |
3B, 7B.6.3 |
$49$ |
\( 2 \cdot 3 \) |
$1$ |
$0.157668741$ |
6.139818101 |
\( \frac{293180476215589246298781}{8} a - \frac{626661132824280747392901}{4} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -2811454 a - 9207370\) , \( 4982304576 a + 16316634679\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-2811454a-9207370\right){x}+4982304576a+16316634679$ |
| 128.5-c3 |
128.5-c |
$4$ |
$21$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{46} \) |
$2.26923$ |
$(a-4), (a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 7$ |
3B, 7B.6.1 |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$3.311043580$ |
6.139818101 |
\( -\frac{699691689}{2097152} a - \frac{307208349}{2097152} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -345 a + 1491\) , \( -6165 a + 26374\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-345a+1491\right){x}-6165a+26374$ |
| 128.5-c4 |
128.5-c |
$4$ |
$21$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{46} \) |
$2.26923$ |
$(a-4), (a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 7$ |
3B, 7B.6.1 |
$1$ |
\( 2 \cdot 3 \cdot 7 \) |
$1$ |
$1.103681193$ |
6.139818101 |
\( \frac{699691689}{2097152} a - \frac{503450019}{1048576} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 8426 a + 27590\) , \( -733568 a - 2402377\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(8426a+27590\right){x}-733568a-2402377$ |
| 128.5-d1 |
128.5-d |
$1$ |
$1$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{18} \) |
$2.26923$ |
$(a-4), (a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.150255957$ |
$16.35510877$ |
2.603980304 |
\( -\frac{4171}{2} a - 5149 \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -54 a - 174\) , \( 437 a + 1433\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-54a-174\right){x}+437a+1433$ |
| 128.5-e1 |
128.5-e |
$1$ |
$1$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{20} \) |
$2.26923$ |
$(a-4), (a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$2.945263517$ |
3.901096829 |
\( -\frac{25991}{32} a - \frac{85779}{16} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 27493 a - 117498\) , \( 6175813 a - 26401054\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(27493a-117498\right){x}+6175813a-26401054$ |
| 128.5-f1 |
128.5-f |
$1$ |
$1$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{24} \) |
$2.26923$ |
$(a-4), (a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Ns |
$1$ |
\( 2 \) |
$1$ |
$7.017877031$ |
1.859081041 |
\( -\frac{27}{8} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -101 a - 320\) , \( -23439 a - 76751\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-101a-320\right){x}-23439a-76751$ |
| 128.5-g1 |
128.5-g |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( - 2^{27} \) |
$2.26923$ |
$(a-4), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1.819506994$ |
$3.836124259$ |
3.698017476 |
\( -\frac{20297286875}{64} a + \frac{43383068421}{32} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 148 a - 632\) , \( 2096 a - 8960\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(148a-632\right){x}+2096a-8960$ |
| 128.5-g2 |
128.5-g |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( - 2^{21} \) |
$2.26923$ |
$(a-4), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.606502331$ |
$11.50837277$ |
3.698017476 |
\( -\frac{489}{4} a + 1841 \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 3 a - 2\) , \( 5 a - 14\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(3a-2\right){x}+5a-14$ |
| 128.5-g3 |
128.5-g |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( - 2^{21} \) |
$2.26923$ |
$(a-4), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1.213004663$ |
$11.50837277$ |
3.698017476 |
\( \frac{489}{4} a + \frac{6875}{4} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -54 a - 165\) , \( 186 a + 617\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-54a-165\right){x}+186a+617$ |
| 128.5-g4 |
128.5-g |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( - 2^{27} \) |
$2.26923$ |
$(a-4), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$3.639013989$ |
$3.836124259$ |
3.698017476 |
\( \frac{20297286875}{64} a + \frac{66468849967}{64} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -3599 a - 11775\) , \( 227847 a + 746187\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-3599a-11775\right){x}+227847a+746187$ |
| 128.5-h1 |
128.5-h |
$1$ |
$1$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{18} \) |
$2.26923$ |
$(a-4), (a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$5.121493389$ |
1.356716742 |
\( -\frac{4171}{2} a - 5149 \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -243 a + 1040\) , \( 374 a - 1597\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-243a+1040\right){x}+374a-1597$ |
| 128.5-i1 |
128.5-i |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( - 2^{27} \) |
$2.26923$ |
$(a-4), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.874986308$ |
$5.204757226$ |
2.412816521 |
\( -\frac{7754659}{1024} a + \frac{9383969}{512} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -63 a - 212\) , \( -827 a - 2711\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-63a-212\right){x}-827a-2711$ |
| 128.5-i2 |
128.5-i |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( - 2^{21} \) |
$2.26923$ |
$(a-4), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.749972617$ |
$5.204757226$ |
2.412816521 |
\( \frac{925430099}{32} a + \frac{1515353487}{16} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -16853 a + 72043\) , \( -180698668 a + 772471846\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-16853a+72043\right){x}-180698668a+772471846$ |
| 128.5-j1 |
128.5-j |
$4$ |
$21$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{22} \) |
$2.26923$ |
$(a-4), (a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 7$ |
3B, 7B.6.3 |
$1$ |
\( 2^{2} \) |
$9.903074376$ |
$0.157668741$ |
1.654505450 |
\( -\frac{293180476215589246298781}{8} a - \frac{960141789432972248487021}{8} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -25303280 a - 82866156\) , \( -134641581530 a - 440940033556\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-25303280a-82866156\right){x}-134641581530a-440940033556$ |
| 128.5-j2 |
128.5-j |
$4$ |
$21$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{22} \) |
$2.26923$ |
$(a-4), (a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 7$ |
3B, 7B.6.3 |
$1$ |
\( 2^{2} \) |
$3.301024792$ |
$0.473006225$ |
1.654505450 |
\( \frac{293180476215589246298781}{8} a - \frac{626661132824280747392901}{4} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 1044512 a - 4465409\) , \( -1129233268 a + 4827376713\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(1044512a-4465409\right){x}-1129233268a+4827376713$ |
| 128.5-j3 |
128.5-j |
$4$ |
$21$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{46} \) |
$2.26923$ |
$(a-4), (a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 7$ |
3B, 7B.6.1 |
$1$ |
\( 2^{2} \) |
$1.414724910$ |
$1.103681193$ |
1.654505450 |
\( -\frac{699691689}{2097152} a - \frac{307208349}{2097152} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -9410 a - 30816\) , \( -1409836 a - 4617096\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-9410a-30816\right){x}-1409836a-4617096$ |
| 128.5-j4 |
128.5-j |
$4$ |
$21$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{46} \) |
$2.26923$ |
$(a-4), (a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 7$ |
3B, 7B.6.1 |
$1$ |
\( 2^{2} \) |
$0.471574970$ |
$3.311043580$ |
1.654505450 |
\( \frac{699691689}{2097152} a - \frac{503450019}{1048576} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 392 a - 1649\) , \( -11804 a + 50489\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(392a-1649\right){x}-11804a+50489$ |
| 128.5-k1 |
128.5-k |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( - 2^{33} \) |
$2.26923$ |
$(a-4), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{2} \) |
$1$ |
$6.755673373$ |
0.894810797 |
\( -\frac{1536003}{4096} a + \frac{3288897}{2048} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 238 a - 1026\) , \( 3021 a - 12919\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(238a-1026\right){x}+3021a-12919$ |
| 128.5-k2 |
128.5-k |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( - 2^{33} \) |
$2.26923$ |
$(a-4), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{2} \) |
$1$ |
$6.755673373$ |
0.894810797 |
\( \frac{1536003}{4096} a + \frac{5041791}{4096} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -5830 a - 19082\) , \( -296423 a - 970751\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-5830a-19082\right){x}-296423a-970751$ |
| 128.5-k3 |
128.5-k |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{30} \) |
$2.26923$ |
$(a-4), (a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3Ns |
$1$ |
\( 2^{3} \) |
$1$ |
$13.51134674$ |
0.894810797 |
\( \frac{2146689}{64} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -16 a - 46\) , \( 47 a + 157\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-16a-46\right){x}+47a+157$ |
| 128.5-k4 |
128.5-k |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{24} \) |
$2.26923$ |
$(a-4), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \) |
$1$ |
$13.51134674$ |
0.894810797 |
\( \frac{8602523649}{8} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -216 a - 766\) , \( 3407 a + 11229\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-216a-766\right){x}+3407a+11229$ |
| 128.5-l1 |
128.5-l |
$1$ |
$1$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{28} \) |
$2.26923$ |
$(a-4), (a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 11 \) |
$0.043571781$ |
$11.22802494$ |
5.702350788 |
\( \frac{247661905}{2048} a - \frac{529274331}{1024} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 7282 a + 23848\) , \( 2815844 a + 9221656\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(7282a+23848\right){x}+2815844a+9221656$ |
| 128.5-m1 |
128.5-m |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( - 2^{27} \) |
$2.26923$ |
$(a-4), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$3.836124259$ |
1.524321212 |
\( -\frac{20297286875}{64} a + \frac{43383068421}{32} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -116563 a - 381726\) , \( -42807859 a - 140192190\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-116563a-381726\right){x}-42807859a-140192190$ |
| 128.5-m2 |
128.5-m |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( - 2^{21} \) |
$2.26923$ |
$(a-4), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$11.50837277$ |
1.524321212 |
\( -\frac{489}{4} a + 1841 \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 5892 a + 19304\) , \( -268068 a - 877896\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(5892a+19304\right){x}-268068a-877896$ |
| 128.5-m3 |
128.5-m |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( - 2^{21} \) |
$2.26923$ |
$(a-4), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$11.50837277$ |
1.524321212 |
\( \frac{489}{4} a + \frac{6875}{4} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -239 a + 1054\) , \( -2265 a + 9718\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-239a+1054\right){x}-2265a+9718$ |
| 128.5-m4 |
128.5-m |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( - 2^{27} \) |
$2.26923$ |
$(a-4), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$3.836124259$ |
1.524321212 |
\( \frac{20297286875}{64} a + \frac{66468849967}{64} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 4816 a - 20556\) , \( -358616 a + 1533088\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(4816a-20556\right){x}-358616a+1533088$ |
| 128.5-n1 |
128.5-n |
$1$ |
$1$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{28} \) |
$2.26923$ |
$(a-4), (a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$1.717356469$ |
0.454938842 |
\( \frac{247661905}{2048} a - \frac{529274331}{1024} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 29 a - 112\) , \( 135 a - 563\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(29a-112\right){x}+135a-563$ |
| 128.5-o1 |
128.5-o |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( - 2^{27} \) |
$2.26923$ |
$(a-4), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$9.380079907$ |
6.212109674 |
\( -\frac{7754659}{1024} a + \frac{9383969}{512} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 4505 a - 19238\) , \( 310653 a - 1327998\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(4505a-19238\right){x}+310653a-1327998$ |
| 128.5-o2 |
128.5-o |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( - 2^{21} \) |
$2.26923$ |
$(a-4), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$9.380079907$ |
6.212109674 |
\( \frac{925430099}{32} a + \frac{1515353487}{16} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -2 a - 6\) , \( 6 a - 29\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-2a-6\right){x}+6a-29$ |
| 128.5-p1 |
128.5-p |
$1$ |
$1$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{24} \) |
$2.26923$ |
$(a-4), (a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Ns |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.113085979$ |
$7.017877031$ |
2.522831998 |
\( -\frac{27}{8} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 2 a - 8\) , \( 204 a - 872\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a-8\right){x}+204a-872$ |
*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.
