| 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 |
| 18.1-a1 |
18.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{5} \cdot 3^{9} \cdot 19^{12} \) |
$3.89144$ |
$(2,a), (3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5S4 |
$1$ |
\( 2 \) |
$1.401897495$ |
$4.041827279$ |
2.144026930 |
\( -\frac{14271}{32} a + \frac{402735}{32} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 97 a - 974\) , \( -3384 a + 16864\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(97a-974\right){x}-3384a+16864$ |
| 18.1-b1 |
18.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{17} \cdot 3^{9} \) |
$3.89144$ |
$(2,a), (3,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5S4 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$4.041827279$ |
3.823437407 |
\( -\frac{14271}{32} a + \frac{402735}{32} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -12 a + 231\) , \( 42 a - 615\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(-12a+231\right){x}+42a-615$ |
| 18.2-a1 |
18.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{5} \cdot 3^{9} \cdot 19^{12} \) |
$3.89144$ |
$(2,a+1), (3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5S4 |
$1$ |
\( 2 \) |
$1.401897495$ |
$4.041827279$ |
2.144026930 |
\( \frac{14271}{32} a + \frac{24279}{2} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -98 a - 876\) , \( 3384 a + 13480\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3+\left(-a+1\right){x}^2+\left(-98a-876\right){x}+3384a+13480$ |
| 18.2-b1 |
18.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{17} \cdot 3^{9} \) |
$3.89144$ |
$(2,a+1), (3,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5S4 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$4.041827279$ |
3.823437407 |
\( \frac{14271}{32} a + \frac{24279}{2} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 12 a + 219\) , \( -42 a - 573\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(-a+1\right){x}^2+\left(12a+219\right){x}-42a-573$ |
| 28.2-a1 |
28.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{16} \cdot 7^{9} \) |
$4.34592$ |
$(2,a), (7,a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 3^{2} \) |
$0.794065895$ |
$2.245498820$ |
3.036114276 |
\( -\frac{56081100407}{40353607} a + \frac{18561146736}{5764801} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 5 a - 5\) , \( -5 a + 1\bigr] \) |
${y}^2={x}^3-a{x}^2+\left(5a-5\right){x}-5a+1$ |
| 28.2-b1 |
28.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{9} \cdot 19^{12} \) |
$4.34592$ |
$(2,a), (7,a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 3^{3} \) |
$1.093156448$ |
$2.245498820$ |
12.53906478 |
\( -\frac{56081100407}{40353607} a + \frac{18561146736}{5764801} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 490 a + 286\) , \( -13486 a - 141767\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+\left(a-1\right){x}^2+\left(490a+286\right){x}-13486a-141767$ |
| 28.5-a1 |
28.5-a |
$1$ |
$1$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
28.5 |
\( 2^{2} \cdot 7 \) |
\( 2^{16} \cdot 7^{9} \) |
$4.34592$ |
$(2,a+1), (7,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 3^{2} \) |
$0.794065895$ |
$2.245498820$ |
3.036114276 |
\( \frac{56081100407}{40353607} a + \frac{73846926745}{40353607} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -5 a\) , \( 5 a - 4\bigr] \) |
${y}^2={x}^3+\left(a-1\right){x}^2-5a{x}+5a-4$ |
| 28.5-b1 |
28.5-b |
$1$ |
$1$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
28.5 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{9} \cdot 19^{12} \) |
$4.34592$ |
$(2,a+1), (7,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 3^{3} \) |
$1.093156448$ |
$2.245498820$ |
12.53906478 |
\( \frac{56081100407}{40353607} a + \frac{73846926745}{40353607} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -547 a + 720\) , \( 13715 a - 97181\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+a{x}^2+\left(-547a+720\right){x}+13715a-97181$ |
| 32.2-a1 |
32.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
32.2 |
\( 2^{5} \) |
\( 2^{34} \) |
$4.49345$ |
$(2,a), (2,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$3.846256139$ |
1.455373382 |
\( \frac{59319}{32} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a - 24\) , \( -12\bigr] \) |
${y}^2={x}^3+\left(a+1\right){x}^2+\left(a-24\right){x}-12$ |
| 32.2-b1 |
32.2-b |
$2$ |
$31$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
32.2 |
\( 2^{5} \) |
\( 2^{44} \) |
$4.49345$ |
$(2,a), (2,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$31$ |
31B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.072790309$ |
1.623719695 |
\( \frac{163433143125}{2147483648} a + \frac{3497463430875}{2147483648} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -2 a + 248\) , \( -10 a - 560\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2+\left(-2a+248\right){x}-10a-560$ |
| 32.2-b2 |
32.2-b |
$2$ |
$31$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
32.2 |
\( 2^{5} \) |
\( 2^{44} \cdot 31^{12} \) |
$4.49345$ |
$(2,a), (2,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$31$ |
31B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.072790309$ |
1.623719695 |
\( -\frac{163433143125}{2147483648} a + \frac{228806035875}{134217728} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -3272 a + 21368\) , \( 142480 a - 1867920\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2+\left(-3272a+21368\right){x}+142480a-1867920$ |
| 32.2-c1 |
32.2-c |
$1$ |
$1$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
32.2 |
\( 2^{5} \) |
\( 2^{22} \cdot 19^{12} \) |
$4.49345$ |
$(2,a), (2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 2 \cdot 5 \) |
$1.253942390$ |
$3.846256139$ |
9.124771894 |
\( \frac{59319}{32} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 36 a + 1221\) , \( -285 a - 8854\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+a{x}^2+\left(36a+1221\right){x}-285a-8854$ |
| 32.2-d1 |
32.2-d |
$2$ |
$31$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
32.2 |
\( 2^{5} \) |
\( 2^{44} \cdot 3^{12} \) |
$4.49345$ |
$(2,a), (2,a+1)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$31$ |
31B |
|
\( 2 \) |
$1$ |
$1.072790309$ |
9.362802331 |
\( \frac{163433143125}{2147483648} a + \frac{3497463430875}{2147483648} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 39 a - 48\) , \( -129 a + 1060\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(-a+1\right){x}^2+\left(39a-48\right){x}-129a+1060$ |
| 32.2-d2 |
32.2-d |
$2$ |
$31$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
32.2 |
\( 2^{5} \) |
\( 2^{44} \cdot 11^{12} \) |
$4.49345$ |
$(2,a), (2,a+1)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$31$ |
31B |
|
\( 2 \cdot 31 \) |
$1$ |
$1.072790309$ |
9.362802331 |
\( -\frac{163433143125}{2147483648} a + \frac{228806035875}{134217728} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 317 a - 3371\) , \( 3793 a + 34506\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+a{x}^2+\left(317a-3371\right){x}+3793a+34506$ |
| 32.5-a1 |
32.5-a |
$2$ |
$31$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
32.5 |
\( 2^{5} \) |
\( 2^{44} \cdot 31^{12} \) |
$4.49345$ |
$(2,a), (2,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$31$ |
31B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.072790309$ |
1.623719695 |
\( \frac{163433143125}{2147483648} a + \frac{3497463430875}{2147483648} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 3272 a + 18096\) , \( -142480 a - 1725440\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(-a-1\right){x}^2+\left(3272a+18096\right){x}-142480a-1725440$ |
| 32.5-a2 |
32.5-a |
$2$ |
$31$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
32.5 |
\( 2^{5} \) |
\( 2^{44} \) |
$4.49345$ |
$(2,a), (2,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$31$ |
31B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.072790309$ |
1.623719695 |
\( -\frac{163433143125}{2147483648} a + \frac{228806035875}{134217728} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 2 a + 246\) , \( 10 a - 570\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(-a-1\right){x}^2+\left(2a+246\right){x}+10a-570$ |
| 32.5-b1 |
32.5-b |
$1$ |
$1$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
32.5 |
\( 2^{5} \) |
\( 2^{34} \) |
$4.49345$ |
$(2,a), (2,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$3.846256139$ |
1.455373382 |
\( \frac{59319}{32} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a - 24\) , \( 12\bigr] \) |
${y}^2={x}^3+\left(-a-1\right){x}^2+\left(a-24\right){x}+12$ |
| 32.5-c1 |
32.5-c |
$2$ |
$31$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
32.5 |
\( 2^{5} \) |
\( 2^{44} \cdot 11^{12} \) |
$4.49345$ |
$(2,a), (2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$31$ |
31B |
$1$ |
\( 2 \cdot 31 \) |
$0.744034533$ |
$1.072790309$ |
9.362802331 |
\( \frac{163433143125}{2147483648} a + \frac{3497463430875}{2147483648} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -372 a - 3110\) , \( -7220 a + 76883\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(-372a-3110\right){x}-7220a+76883$ |
| 32.5-c2 |
32.5-c |
$2$ |
$31$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
32.5 |
\( 2^{5} \) |
\( 2^{44} \cdot 3^{12} \) |
$4.49345$ |
$(2,a), (2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$31$ |
31B |
$1$ |
\( 2 \) |
$23.06507054$ |
$1.072790309$ |
9.362802331 |
\( -\frac{163433143125}{2147483648} a + \frac{228806035875}{134217728} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -39 a - 9\) , \( 129 a + 931\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(-39a-9\right){x}+129a+931$ |
| 32.5-d1 |
32.5-d |
$1$ |
$1$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
32.5 |
\( 2^{5} \) |
\( 2^{22} \cdot 19^{12} \) |
$4.49345$ |
$(2,a), (2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 2 \cdot 5 \) |
$1.253942390$ |
$3.846256139$ |
9.124771894 |
\( \frac{59319}{32} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -91 a + 1201\) , \( 1450 a - 2027\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(-91a+1201\right){x}+1450a-2027$ |
| 48.2-a1 |
48.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
48.2 |
\( 2^{4} \cdot 3 \) |
\( 2^{9} \cdot 3^{13} \) |
$4.97282$ |
$(2,a), (2,a+1), (3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$1.020698423$ |
$6.620467287$ |
5.113900913 |
\( \frac{1373}{6} a - \frac{40664}{3} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 13 a + 263\) , \( -55 a - 357\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+\left(-a+1\right){x}^2+\left(13a+263\right){x}-55a-357$ |
| 48.2-b1 |
48.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
48.2 |
\( 2^{4} \cdot 3 \) |
\( 2^{9} \cdot 3 \) |
$4.97282$ |
$(2,a), (2,a+1), (3,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$9$ |
\( 2 \) |
$1$ |
$6.620467287$ |
11.27294487 |
\( \frac{1373}{6} a - \frac{40664}{3} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -22 a + 183\) , \( 88 a - 197\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(a+1\right){x}^2+\left(-22a+183\right){x}+88a-197$ |
| 48.4-a1 |
48.4-a |
$1$ |
$1$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
48.4 |
\( 2^{4} \cdot 3 \) |
\( 2^{9} \cdot 3^{13} \) |
$4.97282$ |
$(2,a), (2,a+1), (3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$1.020698423$ |
$6.620467287$ |
5.113900913 |
\( -\frac{1373}{6} a - \frac{79955}{6} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -15 a + 276\) , \( 54 a - 412\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-15a+276\right){x}+54a-412$ |
| 48.4-b1 |
48.4-b |
$1$ |
$1$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
48.4 |
\( 2^{4} \cdot 3 \) |
\( 2^{9} \cdot 3 \) |
$4.97282$ |
$(2,a), (2,a+1), (3,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$9$ |
\( 2 \) |
$1$ |
$6.620467287$ |
11.27294487 |
\( -\frac{1373}{6} a - \frac{79955}{6} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -34 a + 215\) , \( 127 a + 235\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a-1\right){x}^2+\left(-34a+215\right){x}+127a+235$ |
| 75.1-a1 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{32} \cdot 5^{2} \) |
$5.55978$ |
$(3,a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$0.558925428$ |
0.105745062 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-110{x}-880$ |
| 75.1-a2 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{2} \cdot 5^{2} \) |
$5.55978$ |
$(3,a+1), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$8.942806850$ |
0.105745062 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2$ |
| 75.1-a3 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{4} \cdot 5^{16} \) |
$5.55978$ |
$(3,a+1), (5)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$1.117850856$ |
0.105745062 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2+35{x}-28$ |
| 75.1-a4 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{8} \cdot 5^{8} \) |
$5.55978$ |
$(3,a+1), (5)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$2.235701712$ |
0.105745062 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-10{x}-10$ |
| 75.1-a5 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{4} \cdot 5^{4} \) |
$5.55978$ |
$(3,a+1), (5)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$4.471403425$ |
0.105745062 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-5{x}+2$ |
| 75.1-a6 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{16} \cdot 5^{4} \) |
$5.55978$ |
$(3,a+1), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$1.117850856$ |
0.105745062 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-135{x}-660$ |
| 75.1-a7 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{2} \cdot 5^{2} \) |
$5.55978$ |
$(3,a+1), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$2.235701712$ |
0.105745062 |
\( \frac{56667352321}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-80{x}+242$ |
| 75.1-a8 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{8} \cdot 5^{2} \) |
$5.55978$ |
$(3,a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$0.558925428$ |
0.105745062 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-2160{x}-39540$ |
| 75.1-b1 |
75.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{44} \cdot 5^{2} \) |
$5.55978$ |
$(3,a+1), (5)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
|
\( 2^{5} \) |
$1$ |
$0.558925428$ |
13.94448768 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -990\) , \( 22765\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-990{x}+22765$ |
| 75.1-b2 |
75.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{14} \cdot 5^{2} \) |
$5.55978$ |
$(3,a+1), (5)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
|
\( 2 \) |
$1$ |
$8.942806850$ |
13.94448768 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 0\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-5$ |
| 75.1-b3 |
75.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{16} \cdot 5^{16} \) |
$5.55978$ |
$(3,a+1), (5)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
|
\( 2^{5} \) |
$1$ |
$1.117850856$ |
13.94448768 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 315\) , \( 1066\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2+315{x}+1066$ |
| 75.1-b4 |
75.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{20} \cdot 5^{8} \) |
$5.55978$ |
$(3,a+1), (5)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
|
\( 2^{5} \) |
$1$ |
$2.235701712$ |
13.94448768 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -90\) , \( 175\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-90{x}+175$ |
| 75.1-b5 |
75.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{16} \cdot 5^{4} \) |
$5.55978$ |
$(3,a+1), (5)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
|
\( 2^{3} \) |
$1$ |
$4.471403425$ |
13.94448768 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -45\) , \( -104\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-45{x}-104$ |
| 75.1-b6 |
75.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{28} \cdot 5^{4} \) |
$5.55978$ |
$(3,a+1), (5)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
|
\( 2^{5} \) |
$1$ |
$1.117850856$ |
13.94448768 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -1215\) , \( 16600\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-1215{x}+16600$ |
| 75.1-b7 |
75.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{14} \cdot 5^{2} \) |
$5.55978$ |
$(3,a+1), (5)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
|
\( 2 \) |
$1$ |
$2.235701712$ |
13.94448768 |
\( \frac{56667352321}{15} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -720\) , \( -7259\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-720{x}-7259$ |
| 75.1-b8 |
75.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{20} \cdot 5^{2} \) |
$5.55978$ |
$(3,a+1), (5)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
|
\( 2^{3} \) |
$1$ |
$0.558925428$ |
13.94448768 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -19440\) , \( 1048135\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-19440{x}+1048135$ |
| 81.1-a1 |
81.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
81.1 |
\( 3^{4} \) |
\( 3^{22} \) |
$5.66779$ |
$(3,a+1)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3, 149$ |
3Cs.1.1, 149Nn.1.49.1 |
|
\( 3 \) |
$1$ |
$2.702876088$ |
1.781817148 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) |
${y}^2+{y}={x}^3-270{x}-1708$ |
| 81.1-a2 |
81.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
81.1 |
\( 3^{4} \) |
\( 3^{10} \) |
$5.66779$ |
$(3,a+1)$ |
$0 \le r \le 1$ |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3, 149$ |
3Cs.1.1, 149Nn.1.49.1 |
|
\( 1 \) |
$1$ |
$2.702876088$ |
1.781817148 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -30\) , \( 63\bigr] \) |
${y}^2+{y}={x}^3-30{x}+63$ |
| 81.1-a3 |
81.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
81.1 |
\( 3^{4} \) |
\( 3^{18} \) |
$5.66779$ |
$(3,a+1)$ |
$0 \le r \le 1$ |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3, 149$ |
3Cs.1.1, 149Nn.1.49.1 |
|
\( 3 \) |
$1$ |
$8.108628264$ |
1.781817148 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -7\bigr] \) |
${y}^2+{y}={x}^3-7$ |
| 81.1-a4 |
81.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
81.1 |
\( 3^{4} \) |
\( 3^{6} \) |
$5.66779$ |
$(3,a+1)$ |
$0 \le r \le 1$ |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3, 149$ |
3Cs.1.1, 149Nn.1.49.1 |
|
\( 1 \) |
$1$ |
$8.108628264$ |
1.781817148 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{y}={x}^3$ |
| 84.3-a1 |
84.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
84.3 |
\( 2^{2} \cdot 3 \cdot 7 \) |
\( 2^{22} \cdot 3^{2} \cdot 7^{6} \cdot 11^{12} \) |
$5.71955$ |
$(2,a), (2,a+1), (3,a+1), (7,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.072109768$ |
1.217017247 |
\( -\frac{513976740875609}{740183506944} a - \frac{9377644369457815}{740183506944} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( 148 a - 7879\) , \( 8643 a - 277062\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^3+\left(148a-7879\right){x}+8643a-277062$ |
| 84.3-a2 |
84.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
84.3 |
\( 2^{2} \cdot 3 \cdot 7 \) |
\( 2^{10} \cdot 3^{6} \cdot 7^{2} \cdot 11^{12} \) |
$5.71955$ |
$(2,a), (2,a+1), (3,a+1), (7,a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$3.216329305$ |
1.217017247 |
\( -\frac{349747}{56448} a + \frac{301212601}{169344} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -17 a + 536\) , \( -63 a - 762\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^3+\left(-17a+536\right){x}-63a-762$ |
| 84.3-b1 |
84.3-b |
$2$ |
$3$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
84.3 |
\( 2^{2} \cdot 3 \cdot 7 \) |
\( 2^{22} \cdot 3^{2} \cdot 7^{6} \cdot 31^{12} \) |
$5.71955$ |
$(2,a), (2,a+1), (3,a+1), (7,a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \cdot 7 \) |
$0.670512910$ |
$1.072109768$ |
3.808120290 |
\( -\frac{513976740875609}{740183506944} a - \frac{9377644369457815}{740183506944} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -2609 a + 58159\) , \( -444491 a - 3837647\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(a-1\right){x}^2+\left(-2609a+58159\right){x}-444491a-3837647$ |
| 84.3-b2 |
84.3-b |
$2$ |
$3$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
84.3 |
\( 2^{2} \cdot 3 \cdot 7 \) |
\( 2^{10} \cdot 3^{6} \cdot 7^{2} \cdot 31^{12} \) |
$5.71955$ |
$(2,a), (2,a+1), (3,a+1), (7,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \cdot 7 \) |
$0.223504303$ |
$3.216329305$ |
3.808120290 |
\( -\frac{349747}{56448} a + \frac{301212601}{169344} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 226 a - 3866\) , \( -3467 a - 167\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(a-1\right){x}^2+\left(226a-3866\right){x}-3467a-167$ |
| 84.4-a1 |
84.4-a |
$2$ |
$3$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
84.4 |
\( 2^{2} \cdot 3 \cdot 7 \) |
\( 2^{22} \cdot 3^{2} \cdot 7^{6} \cdot 31^{12} \) |
$5.71955$ |
$(2,a), (2,a+1), (3,a+1), (7,a+6)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \cdot 7 \) |
$0.670512910$ |
$1.072109768$ |
3.808120290 |
\( \frac{513976740875609}{740183506944} a - \frac{29439348542659}{2202927104} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 2609 a + 55550\) , \( 444491 a - 4282138\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-a{x}^2+\left(2609a+55550\right){x}+444491a-4282138$ |
| 84.4-a2 |
84.4-a |
$2$ |
$3$ |
\(\Q(\sqrt{-447}) \) |
$2$ |
$[0, 1]$ |
84.4 |
\( 2^{2} \cdot 3 \cdot 7 \) |
\( 2^{10} \cdot 3^{6} \cdot 7^{2} \cdot 31^{12} \) |
$5.71955$ |
$(2,a), (2,a+1), (3,a+1), (7,a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \cdot 7 \) |
$0.223504303$ |
$3.216329305$ |
3.808120290 |
\( \frac{349747}{56448} a + \frac{1340015}{756} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( -226 a - 3640\) , \( 3467 a - 3634\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-a{x}^2+\left(-226a-3640\right){x}+3467a-3634$ |
*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.
