| 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 |
| 8064.4-a1 |
8064.4-a |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8064.4 |
\( 2^{7} \cdot 3^{2} \cdot 7 \) |
\( 2^{12} \cdot 3^{2} \cdot 7^{6} \) |
$2.24040$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.161678695$ |
1.634075498 |
\( -\frac{30704}{1029} a + \frac{1824160}{1029} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 8 a - 4\) , \( a - 7\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(8a-4\right){x}+a-7$ |
| 8064.4-a2 |
8064.4-a |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8064.4 |
\( 2^{7} \cdot 3^{2} \cdot 7 \) |
\( 2^{12} \cdot 3^{4} \cdot 7^{3} \) |
$2.24040$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.161678695$ |
1.634075498 |
\( \frac{4565872}{147} a + \frac{68482448}{441} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 2 a + 24\) , \( 29 a - 18\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a+24\right){x}+29a-18$ |
| 8064.4-b1 |
8064.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8064.4 |
\( 2^{7} \cdot 3^{2} \cdot 7 \) |
\( 2^{20} \cdot 3^{2} \cdot 7 \) |
$2.24040$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.971756568$ |
$1.254911473$ |
3.687326055 |
\( \frac{6193144}{21} a - \frac{1390346492}{21} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -128 a + 64\) , \( 412 a - 804\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-128a+64\right){x}+412a-804$ |
| 8064.4-b2 |
8064.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8064.4 |
\( 2^{7} \cdot 3^{2} \cdot 7 \) |
\( 2^{14} \cdot 3^{8} \cdot 7 \) |
$2.24040$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.971756568$ |
$2.509822947$ |
3.687326055 |
\( -\frac{17252}{63} a - \frac{89876}{567} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2 a + 4\) , \( a - 6\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a+4\right){x}+a-6$ |
| 8064.4-b3 |
8064.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8064.4 |
\( 2^{7} \cdot 3^{2} \cdot 7 \) |
\( 2^{16} \cdot 3^{4} \cdot 7^{2} \) |
$2.24040$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.485878284$ |
$2.509822947$ |
3.687326055 |
\( \frac{42880}{7} a - \frac{20656}{9} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -8 a + 4\) , \( 4 a - 12\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-8a+4\right){x}+4a-12$ |
| 8064.4-b4 |
8064.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8064.4 |
\( 2^{7} \cdot 3^{2} \cdot 7 \) |
\( 2^{14} \cdot 3^{2} \cdot 7^{4} \) |
$2.24040$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.971756568$ |
$2.509822947$ |
3.687326055 |
\( -\frac{546100}{147} a + \frac{447416}{147} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -4 a + 9\) , \( -2 a - 16\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a+9\right){x}-2a-16$ |
| 8064.4-c1 |
8064.4-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8064.4 |
\( 2^{7} \cdot 3^{2} \cdot 7 \) |
\( 2^{16} \cdot 3^{4} \cdot 7 \) |
$2.24040$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$1.402443500$ |
2.120295274 |
\( -\frac{863944673}{63} a - \frac{1616364293}{63} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 93 a - 78\) , \( 414 a\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(93a-78\right){x}+414a$ |
| 8064.4-c2 |
8064.4-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8064.4 |
\( 2^{7} \cdot 3^{2} \cdot 7 \) |
\( 2^{23} \cdot 3^{2} \cdot 7^{8} \) |
$2.24040$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.701221750$ |
2.120295274 |
\( \frac{70011793}{7203} a - \frac{221078161}{7203} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 128 a - 16\) , \( 220 a + 728\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(128a-16\right){x}+220a+728$ |
| 8064.4-c3 |
8064.4-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8064.4 |
\( 2^{7} \cdot 3^{2} \cdot 7 \) |
\( 2^{22} \cdot 3^{4} \cdot 7^{4} \) |
$2.24040$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.402443500$ |
2.120295274 |
\( \frac{172799}{441} a - \frac{2545}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 8 a - 16\) , \( -20 a + 56\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(8a-16\right){x}-20a+56$ |
| 8064.4-c4 |
8064.4-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8064.4 |
\( 2^{7} \cdot 3^{2} \cdot 7 \) |
\( 2^{20} \cdot 3^{8} \cdot 7^{2} \) |
$2.24040$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$1.402443500$ |
2.120295274 |
\( -\frac{839201}{189} a + \frac{2555873}{567} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -3 a - 30\) , \( 18 a + 72\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3a-30\right){x}+18a+72$ |
| 8064.4-c5 |
8064.4-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8064.4 |
\( 2^{7} \cdot 3^{2} \cdot 7 \) |
\( 2^{22} \cdot 3^{16} \cdot 7 \) |
$2.24040$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.701221750$ |
2.120295274 |
\( \frac{78717967}{15309} a - \frac{9092939}{45927} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -63 a - 70\) , \( -330 a - 48\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-63a-70\right){x}-330a-48$ |
| 8064.4-c6 |
8064.4-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8064.4 |
\( 2^{7} \cdot 3^{2} \cdot 7 \) |
\( 2^{23} \cdot 3^{2} \cdot 7^{2} \) |
$2.24040$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.402443500$ |
2.120295274 |
\( -\frac{13784383}{21} a + \frac{8018911}{21} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -47 a - 22\) , \( -238 a + 84\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-47a-22\right){x}-238a+84$ |
| 8064.4-d1 |
8064.4-d |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8064.4 |
\( 2^{7} \cdot 3^{2} \cdot 7 \) |
\( 2^{8} \cdot 3^{6} \cdot 7^{2} \) |
$2.24040$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.072656234$ |
2.322709788 |
\( \frac{1116160}{189} a - \frac{5451776}{189} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -a + 9\) , \( -5 a\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-a+9\right){x}-5a$ |
| 8064.4-d2 |
8064.4-d |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8064.4 |
\( 2^{7} \cdot 3^{2} \cdot 7 \) |
\( 2^{16} \cdot 3^{12} \cdot 7 \) |
$2.24040$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.536328117$ |
2.322709788 |
\( -\frac{49568}{63} a + \frac{2715344}{5103} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -11 a + 14\) , \( -8 a + 40\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-11a+14\right){x}-8a+40$ |
| 8064.4-e1 |
8064.4-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8064.4 |
\( 2^{7} \cdot 3^{2} \cdot 7 \) |
\( 2^{20} \cdot 3^{2} \cdot 7 \) |
$2.24040$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.901291163$ |
$1.254911473$ |
3.607220506 |
\( -\frac{6193144}{21} a - \frac{1384153348}{21} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 128 a - 64\) , \( 412 a + 392\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(128a-64\right){x}+412a+392$ |
| 8064.4-e2 |
8064.4-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8064.4 |
\( 2^{7} \cdot 3^{2} \cdot 7 \) |
\( 2^{14} \cdot 3^{8} \cdot 7 \) |
$2.24040$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.475322790$ |
$2.509822947$ |
3.607220506 |
\( \frac{17252}{63} a - \frac{245144}{567} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4 a + 1\) , \( 4 a + 6\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(4a+1\right){x}+4a+6$ |
| 8064.4-e3 |
8064.4-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8064.4 |
\( 2^{7} \cdot 3^{2} \cdot 7 \) |
\( 2^{16} \cdot 3^{4} \cdot 7^{2} \) |
$2.24040$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.950645581$ |
$2.509822947$ |
3.607220506 |
\( -\frac{42880}{7} a + \frac{241328}{63} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 8 a - 4\) , \( 4 a + 8\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(8a-4\right){x}+4a+8$ |
| 8064.4-e4 |
8064.4-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8064.4 |
\( 2^{7} \cdot 3^{2} \cdot 7 \) |
\( 2^{14} \cdot 3^{2} \cdot 7^{4} \) |
$2.24040$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.475322790$ |
$2.509822947$ |
3.607220506 |
\( \frac{546100}{147} a - \frac{98684}{147} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 6 a + 4\) , \( -7 a + 14\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(6a+4\right){x}-7a+14$ |
| 8064.4-f1 |
8064.4-f |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8064.4 |
\( 2^{7} \cdot 3^{2} \cdot 7 \) |
\( 2^{22} \cdot 3^{8} \cdot 7 \) |
$2.24040$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.545461846$ |
$1.097685804$ |
3.620873802 |
\( \frac{48284377}{189} a - \frac{108521789}{567} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 64 a + 40\) , \( -68 a + 492\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(64a+40\right){x}-68a+492$ |
| 8064.4-f2 |
8064.4-f |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8064.4 |
\( 2^{7} \cdot 3^{2} \cdot 7 \) |
\( 2^{22} \cdot 3^{2} \cdot 7 \) |
$2.24040$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.545461846$ |
$2.195371609$ |
3.620873802 |
\( -\frac{219127}{7} a - \frac{566221}{21} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -7 a - 14\) , \( -10 a - 16\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-7a-14\right){x}-10a-16$ |
| 8064.4-f3 |
8064.4-f |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8064.4 |
\( 2^{7} \cdot 3^{2} \cdot 7 \) |
\( 2^{20} \cdot 3^{4} \cdot 7^{2} \) |
$2.24040$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.272730923$ |
$2.195371609$ |
3.620873802 |
\( -\frac{4009}{21} a + \frac{2191}{9} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 4 a\) , \( -4 a + 12\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+4a{x}-4a+12$ |
| 8064.4-f4 |
8064.4-f |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8064.4 |
\( 2^{7} \cdot 3^{2} \cdot 7 \) |
\( 2^{16} \cdot 3^{2} \cdot 7^{4} \) |
$2.24040$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.545461846$ |
$2.195371609$ |
3.620873802 |
\( \frac{166231}{49} a + \frac{660025}{147} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2 a - 12\) , \( a + 10\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a-12\right){x}+a+10$ |
*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.
