| 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 |
| 36.1-a1 |
36.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{6} \cdot 3^{3} \) |
$1.65254$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$1$ |
$8.446639215$ |
4.475138779 |
\( -\frac{881361}{16} a + \frac{3765231}{16} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -2 a - 7\) , \( -10 a - 33\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-2a-7\right){x}-10a-33$ |
| 36.1-a2 |
36.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{18} \cdot 3^{9} \) |
$1.65254$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$8.446639215$ |
4.475138779 |
\( -\frac{5470725}{4096} a + \frac{23991063}{4096} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 18 a + 58\) , \( 258 a + 845\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(18a+58\right){x}+258a+845$ |
| 36.1-a3 |
36.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{18} \cdot 3^{9} \) |
$1.65254$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$8.446639215$ |
4.475138779 |
\( \frac{5470725}{4096} a + \frac{9260169}{2048} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -18 a + 76\) , \( -258 a + 1103\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-18a+76\right){x}-258a+1103$ |
| 36.1-a4 |
36.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{6} \cdot 3^{3} \) |
$1.65254$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$1$ |
$8.446639215$ |
4.475138779 |
\( \frac{881361}{16} a + \frac{1441935}{8} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 2 a - 9\) , \( 10 a - 43\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(2a-9\right){x}+10a-43$ |
| 36.1-b1 |
36.1-b |
$4$ |
$21$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{6} \) |
$1.65254$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 7$ |
3B.1.2, 7B.6.3 |
$49$ |
\( 1 \) |
$1$ |
$0.257471977$ |
1.671046829 |
\( -\frac{293180476215589246298781}{8} a - \frac{960141789432972248487021}{8} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 64690450 a - 276546321\) , \( -550295059294 a + 2352465823751\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(64690450a-276546321\right){x}-550295059294a+2352465823751$ |
| 36.1-b2 |
36.1-b |
$4$ |
$21$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{6} \) |
$1.65254$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 7$ |
3B.1.1, 7B.6.3 |
$49$ |
\( 3 \) |
$1$ |
$0.772415932$ |
1.671046829 |
\( \frac{293180476215589246298781}{8} a - \frac{626661132824280747392901}{4} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 5674 a - 29613\) , \( -560830 a + 2247997\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(5674a-29613\right){x}-560830a+2247997$ |
| 36.1-b3 |
36.1-b |
$4$ |
$21$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{28} \cdot 3^{6} \) |
$1.65254$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 7$ |
3B.1.2, 7B.6.1 |
$1$ |
\( 7 \) |
$1$ |
$1.802303842$ |
1.671046829 |
\( -\frac{699691689}{2097152} a - \frac{307208349}{2097152} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -193880 a + 828819\) , \( 82120562 a - 351058609\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-193880a+828819\right){x}+82120562a-351058609$ |
| 36.1-b4 |
36.1-b |
$4$ |
$21$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{28} \cdot 3^{6} \) |
$1.65254$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 7$ |
3B.1.1, 7B.6.1 |
$1$ |
\( 3 \cdot 7 \) |
$1$ |
$5.406911526$ |
1.671046829 |
\( \frac{699691689}{2097152} a - \frac{503450019}{1048576} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 4 a - 3\) , \( -4 a + 31\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(4a-3\right){x}-4a+31$ |
| 36.1-c1 |
36.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{6} \cdot 3^{3} \) |
$1.65254$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \) |
$1$ |
$35.80333605$ |
1.053837268 |
\( -\frac{881361}{16} a + \frac{3765231}{16} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 1663 a - 7109\) , \( -71989 a + 307747\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(1663a-7109\right){x}-71989a+307747$ |
| 36.1-c2 |
36.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{18} \cdot 3^{9} \) |
$1.65254$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$3.978148450$ |
1.053837268 |
\( -\frac{5470725}{4096} a + \frac{23991063}{4096} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 7683 a - 32844\) , \( 647373 a - 2767466\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(7683a-32844\right){x}+647373a-2767466$ |
| 36.1-c3 |
36.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{18} \cdot 3^{9} \) |
$1.65254$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$3.978148450$ |
1.053837268 |
\( \frac{5470725}{4096} a + \frac{9260169}{2048} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -7683 a - 25161\) , \( -647373 a - 2120093\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-7683a-25161\right){x}-647373a-2120093$ |
| 36.1-c4 |
36.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{6} \cdot 3^{3} \) |
$1.65254$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \) |
$1$ |
$35.80333605$ |
1.053837268 |
\( \frac{881361}{16} a + \frac{1441935}{8} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -1663 a - 5446\) , \( 71989 a + 235758\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-1663a-5446\right){x}+71989a+235758$ |
| 36.1-d1 |
36.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{9} \cdot 3^{6} \) |
$1.65254$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$6.264364683$ |
2.489206115 |
\( -\frac{20297286875}{64} a + \frac{43383068421}{32} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 82777 a - 353858\) , \( -25270511 a + 108029346\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(82777a-353858\right){x}-25270511a+108029346$ |
| 36.1-d2 |
36.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{3} \cdot 3^{6} \) |
$1.65254$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$18.79309404$ |
2.489206115 |
\( -\frac{489}{4} a + 1841 \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 1207 a - 5153\) , \( -22427 a + 95877\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(1207a-5153\right){x}-22427a+95877$ |
| 36.1-d3 |
36.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{3} \cdot 3^{6} \) |
$1.65254$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$18.79309404$ |
2.489206115 |
\( \frac{489}{4} a + \frac{6875}{4} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -a + 11\) , \( a - 1\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-a+11\right){x}+a-1$ |
| 36.1-d4 |
36.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{9} \cdot 3^{6} \) |
$1.65254$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$6.264364683$ |
2.489206115 |
\( \frac{20297286875}{64} a + \frac{66468849967}{64} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 29 a - 124\) , \( -203 a + 854\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(29a-124\right){x}-203a+854$ |
| 36.1-e1 |
36.1-e |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{6} \cdot 3^{9} \) |
$1.65254$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.244838978$ |
$10.04021683$ |
2.604810953 |
\( -\frac{881361}{16} a + \frac{3765231}{16} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 16 a - 71\) , \( 66 a - 289\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(16a-71\right){x}+66a-289$ |
| 36.1-e2 |
36.1-e |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{18} \cdot 3^{3} \) |
$1.65254$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.081612992$ |
$10.04021683$ |
2.604810953 |
\( -\frac{5470725}{4096} a + \frac{23991063}{4096} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 1804 a + 5911\) , \( -262428 a - 859431\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(1804a+5911\right){x}-262428a-859431$ |
| 36.1-e3 |
36.1-e |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{18} \cdot 3^{3} \) |
$1.65254$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.163225985$ |
$10.04021683$ |
2.604810953 |
\( \frac{5470725}{4096} a + \frac{9260169}{2048} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -8 a - 23\) , \( -36 a - 119\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-8a-23\right){x}-36a-119$ |
| 36.1-e4 |
36.1-e |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{6} \cdot 3^{9} \) |
$1.65254$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.489677956$ |
$10.04021683$ |
2.604810953 |
\( \frac{881361}{16} a + \frac{1441935}{8} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 1828 a - 7817\) , \( 285948 a - 1222411\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(1828a-7817\right){x}+285948a-1222411$ |
| 36.1-f1 |
36.1-f |
$4$ |
$21$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{6} \) |
$1.65254$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 7$ |
3B.1.1, 7B.6.3 |
$49$ |
\( 3 \) |
$1$ |
$0.772415932$ |
1.671046829 |
\( -\frac{293180476215589246298781}{8} a - \frac{960141789432972248487021}{8} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -5675 a - 23939\) , \( 560829 a + 1687167\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-5675a-23939\right){x}+560829a+1687167$ |
| 36.1-f2 |
36.1-f |
$4$ |
$21$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{6} \) |
$1.65254$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 7$ |
3B.1.2, 7B.6.3 |
$49$ |
\( 1 \) |
$1$ |
$0.257471977$ |
1.671046829 |
\( \frac{293180476215589246298781}{8} a - \frac{626661132824280747392901}{4} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -64690451 a - 211855871\) , \( 550295059293 a + 1802170764457\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-64690451a-211855871\right){x}+550295059293a+1802170764457$ |
| 36.1-f3 |
36.1-f |
$4$ |
$21$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{28} \cdot 3^{6} \) |
$1.65254$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 7$ |
3B.1.1, 7B.6.1 |
$1$ |
\( 3 \cdot 7 \) |
$1$ |
$5.406911526$ |
1.671046829 |
\( -\frac{699691689}{2097152} a - \frac{307208349}{2097152} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -5 a + 1\) , \( 3 a + 27\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-5a+1\right){x}+3a+27$ |
| 36.1-f4 |
36.1-f |
$4$ |
$21$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{28} \cdot 3^{6} \) |
$1.65254$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 7$ |
3B.1.2, 7B.6.1 |
$1$ |
\( 7 \) |
$1$ |
$1.802303842$ |
1.671046829 |
\( \frac{699691689}{2097152} a - \frac{503450019}{1048576} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 193879 a + 634939\) , \( -82120563 a - 268938047\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(193879a+634939\right){x}-82120563a-268938047$ |
| 36.1-g1 |
36.1-g |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{9} \cdot 3^{6} \) |
$1.65254$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$6.264364683$ |
2.489206115 |
\( -\frac{20297286875}{64} a + \frac{43383068421}{32} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -29 a - 95\) , \( 203 a + 651\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-29a-95\right){x}+203a+651$ |
| 36.1-g2 |
36.1-g |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{3} \cdot 3^{6} \) |
$1.65254$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$18.79309404$ |
2.489206115 |
\( -\frac{489}{4} a + 1841 \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( a + 10\) , \( -a\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(a+10\right){x}-a$ |
| 36.1-g3 |
36.1-g |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{3} \cdot 3^{6} \) |
$1.65254$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$18.79309404$ |
2.489206115 |
\( \frac{489}{4} a + \frac{6875}{4} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -1207 a - 3946\) , \( 22427 a + 73450\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1207a-3946\right){x}+22427a+73450$ |
| 36.1-g4 |
36.1-g |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{9} \cdot 3^{6} \) |
$1.65254$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$6.264364683$ |
2.489206115 |
\( \frac{20297286875}{64} a + \frac{66468849967}{64} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -82777 a - 271081\) , \( 25270511 a + 82758835\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-82777a-271081\right){x}+25270511a+82758835$ |
| 36.1-h1 |
36.1-h |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{6} \cdot 3^{9} \) |
$1.65254$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.489677956$ |
$10.04021683$ |
2.604810953 |
\( -\frac{881361}{16} a + \frac{3765231}{16} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -1829 a - 5988\) , \( -285949 a - 936462\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-1829a-5988\right){x}-285949a-936462$ |
| 36.1-h2 |
36.1-h |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{18} \cdot 3^{3} \) |
$1.65254$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.163225985$ |
$10.04021683$ |
2.604810953 |
\( -\frac{5470725}{4096} a + \frac{23991063}{4096} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 8 a - 31\) , \( 36 a - 155\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(8a-31\right){x}+36a-155$ |
| 36.1-h3 |
36.1-h |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{18} \cdot 3^{3} \) |
$1.65254$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.081612992$ |
$10.04021683$ |
2.604810953 |
\( \frac{5470725}{4096} a + \frac{9260169}{2048} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -1804 a + 7715\) , \( 262428 a - 1121859\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1804a+7715\right){x}+262428a-1121859$ |
| 36.1-h4 |
36.1-h |
$4$ |
$6$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{6} \cdot 3^{9} \) |
$1.65254$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.244838978$ |
$10.04021683$ |
2.604810953 |
\( \frac{881361}{16} a + \frac{1441935}{8} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -17 a - 54\) , \( -67 a - 222\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-17a-54\right){x}-67a-222$ |
*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.
