| 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 |
| 4096.7-CMb1 |
4096.7-CMb |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{36} \) |
$1.89137$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$1$ |
$1.635241191$ |
1.236126150 |
\( -3375 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 20\) , \( -32 a + 16\bigr] \) |
${y}^2={x}^{3}+20{x}-32a+16$ |
| 4096.7-CMb2 |
4096.7-CMb |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{36} \) |
$1.89137$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-28$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$0.817620595$ |
1.236126150 |
\( 16581375 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 340\) , \( -1824 a + 912\bigr] \) |
${y}^2={x}^{3}+340{x}-1824a+912$ |
| 4096.7-CMa1 |
4096.7-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{36} \) |
$1.89137$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$1$ |
$1.635241191$ |
1.236126150 |
\( -3375 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 20\) , \( 32 a - 16\bigr] \) |
${y}^2={x}^{3}+20{x}+32a-16$ |
| 4096.7-CMa2 |
4096.7-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{36} \) |
$1.89137$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-28$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$0.817620595$ |
1.236126150 |
\( 16581375 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 340\) , \( 1824 a - 912\bigr] \) |
${y}^2={x}^{3}+340{x}+1824a-912$ |
| 4096.7-a1 |
4096.7-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{31} \) |
$1.89137$ |
$(a), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.160998220$ |
$1.540617835$ |
2.704191521 |
\( -237572 a - 285952 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -43 a + 41\) , \( -23 a + 205\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-43a+41\right){x}-23a+205$ |
| 4096.7-a2 |
4096.7-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{22} \) |
$1.89137$ |
$(a), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.160998220$ |
$3.081235671$ |
2.704191521 |
\( 3084 a - 65800 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -6 a + 9\) , \( a + 8\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-6a+9\right){x}+a+8$ |
| 4096.7-a3 |
4096.7-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{26} \) |
$1.89137$ |
$(a), (-a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.580499110$ |
$3.081235671$ |
2.704191521 |
\( 336 a + 224 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -3 a + 1\) , \( a + 5\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-3a+1\right){x}+a+5$ |
| 4096.7-a4 |
4096.7-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{25} \) |
$1.89137$ |
$(a), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.290249555$ |
$3.081235671$ |
2.704191521 |
\( -2056 a + 4824 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -a + 6\) , \( 5 a + 2\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-a+6\right){x}+5a+2$ |
| 4096.7-b1 |
4096.7-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{31} \) |
$1.89137$ |
$(a), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.160998220$ |
$1.540617835$ |
2.704191521 |
\( 237572 a - 523524 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 43 a - 2\) , \( 23 a + 182\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(43a-2\right){x}+23a+182$ |
| 4096.7-b2 |
4096.7-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{22} \) |
$1.89137$ |
$(a), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.160998220$ |
$3.081235671$ |
2.704191521 |
\( -3084 a - 62716 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 6 a + 3\) , \( -a + 9\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(6a+3\right){x}-a+9$ |
| 4096.7-b3 |
4096.7-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{26} \) |
$1.89137$ |
$(a), (-a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.580499110$ |
$3.081235671$ |
2.704191521 |
\( -336 a + 560 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 3 a - 2\) , \( -a + 6\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(3a-2\right){x}-a+6$ |
| 4096.7-b4 |
4096.7-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{25} \) |
$1.89137$ |
$(a), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.290249555$ |
$3.081235671$ |
2.704191521 |
\( 2056 a + 2768 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( a + 5\) , \( -5 a + 7\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(a+5\right){x}-5a+7$ |
| 4096.7-c1 |
4096.7-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{12} \) |
$1.89137$ |
$(a), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 1 \) |
$1.067060424$ |
$6.875185818$ |
2.772837593 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}$ |
| 4096.7-c2 |
4096.7-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{24} \) |
$1.89137$ |
$(a), (-a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.533530212$ |
$3.437592909$ |
2.772837593 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4\) , \( 0\bigr] \) |
${y}^2={x}^{3}-4{x}$ |
| 4096.7-c3 |
4096.7-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{30} \) |
$1.89137$ |
$(a), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1.067060424$ |
$1.718796454$ |
2.772837593 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -44\) , \( -112\bigr] \) |
${y}^2={x}^{3}-44{x}-112$ |
| 4096.7-c4 |
4096.7-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{30} \) |
$1.89137$ |
$(a), (-a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$1.067060424$ |
$1.718796454$ |
2.772837593 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -44\) , \( 112\bigr] \) |
${y}^2={x}^{3}-44{x}+112$ |
| 4096.7-d1 |
4096.7-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{24} \) |
$1.89137$ |
$(a), (-a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2Cs, 3Nn |
$1$ |
\( 2^{4} \) |
$0.561107826$ |
$3.493963323$ |
2.963982530 |
\( -64 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 1\) , \( -3 a + 1\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+1\right){x}-3a+1$ |
| 4096.7-d2 |
4096.7-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{21} \) |
$1.89137$ |
$(a), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2 \) |
$1.122215653$ |
$3.493963323$ |
2.963982530 |
\( -17416 a + 20208 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -a - 6\) , \( -a - 4\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-a-6\right){x}-a-4$ |
| 4096.7-d3 |
4096.7-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{21} \) |
$1.89137$ |
$(a), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2 \) |
$1.122215653$ |
$3.493963323$ |
2.963982530 |
\( 17416 a + 2792 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( a - 7\) , \( -a + 5\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(a-7\right){x}-a+5$ |
| 4096.7-d4 |
4096.7-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{30} \) |
$1.89137$ |
$(a), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2^{2} \) |
$1.122215653$ |
$1.746981661$ |
2.963982530 |
\( 238328 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 41\) , \( -91 a + 25\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+41\right){x}-91a+25$ |
| 4096.7-e1 |
4096.7-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{24} \) |
$1.89137$ |
$(a), (-a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2Cs, 3Nn |
$1$ |
\( 2^{4} \) |
$0.561107826$ |
$3.493963323$ |
2.963982530 |
\( -64 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 1\) , \( 3 a - 1\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+1\right){x}+3a-1$ |
| 4096.7-e2 |
4096.7-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{21} \) |
$1.89137$ |
$(a), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2 \) |
$1.122215653$ |
$3.493963323$ |
2.963982530 |
\( -17416 a + 20208 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -a - 6\) , \( a + 4\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-a-6\right){x}+a+4$ |
| 4096.7-e3 |
4096.7-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{21} \) |
$1.89137$ |
$(a), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2 \) |
$1.122215653$ |
$3.493963323$ |
2.963982530 |
\( 17416 a + 2792 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( a - 7\) , \( a - 5\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(a-7\right){x}+a-5$ |
| 4096.7-e4 |
4096.7-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{30} \) |
$1.89137$ |
$(a), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2^{2} \) |
$1.122215653$ |
$1.746981661$ |
2.963982530 |
\( 238328 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 41\) , \( 91 a - 25\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+41\right){x}+91a-25$ |
| 4096.7-f1 |
4096.7-f |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{33} \) |
$1.89137$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 5$ |
2B, 5S4 |
$1$ |
\( 2^{3} \) |
$1$ |
$1.200251720$ |
1.814610036 |
\( -1097726 a - 998656 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 85 a - 87\) , \( -407 a + 45\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(85a-87\right){x}-407a+45$ |
| 4096.7-f2 |
4096.7-f |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{33} \) |
$1.89137$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 5$ |
2B, 5S4 |
$1$ |
\( 2^{3} \) |
$1$ |
$1.200251720$ |
1.814610036 |
\( 1097726 a - 2096382 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -85 a - 2\) , \( -407 a + 362\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-85a-2\right){x}-407a+362$ |
| 4096.7-f3 |
4096.7-f |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{27} \) |
$1.89137$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 5$ |
2B, 5S4 |
$1$ |
\( 2^{2} \) |
$1$ |
$2.400503441$ |
1.814610036 |
\( -28658 a + 8966 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 9 a - 15\) , \( 23 a - 13\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(9a-15\right){x}+23a-13$ |
| 4096.7-f4 |
4096.7-f |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{27} \) |
$1.89137$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 5$ |
2B, 5S4 |
$1$ |
\( 2^{2} \) |
$1$ |
$2.400503441$ |
1.814610036 |
\( 28658 a - 19692 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -9 a - 6\) , \( 23 a - 10\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-9a-6\right){x}+23a-10$ |
| 4096.7-f5 |
4096.7-f |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{30} \) |
$1.89137$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 5$ |
2Cs, 5S4 |
$1$ |
\( 2^{4} \) |
$1$ |
$2.400503441$ |
1.814610036 |
\( -924 a + 1784 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 5 a - 7\) , \( -7 a - 3\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(5a-7\right){x}-7a-3$ |
| 4096.7-f6 |
4096.7-f |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{30} \) |
$1.89137$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 5$ |
2Cs, 5S4 |
$1$ |
\( 2^{4} \) |
$1$ |
$2.400503441$ |
1.814610036 |
\( 924 a + 860 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -5 a - 2\) , \( -7 a + 10\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-5a-2\right){x}-7a+10$ |
| 4096.7-g1 |
4096.7-g |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{33} \) |
$1.89137$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 5$ |
2B, 5S4 |
$1$ |
\( 2^{3} \) |
$1$ |
$1.200251720$ |
1.814610036 |
\( -1097726 a - 998656 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 85 a - 87\) , \( 407 a - 45\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(85a-87\right){x}+407a-45$ |
| 4096.7-g2 |
4096.7-g |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{33} \) |
$1.89137$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 5$ |
2B, 5S4 |
$1$ |
\( 2^{3} \) |
$1$ |
$1.200251720$ |
1.814610036 |
\( 1097726 a - 2096382 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -85 a - 2\) , \( 407 a - 362\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-85a-2\right){x}+407a-362$ |
| 4096.7-g3 |
4096.7-g |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{27} \) |
$1.89137$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 5$ |
2B, 5S4 |
$1$ |
\( 2^{2} \) |
$1$ |
$2.400503441$ |
1.814610036 |
\( -28658 a + 8966 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 9 a - 15\) , \( -23 a + 13\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(9a-15\right){x}-23a+13$ |
| 4096.7-g4 |
4096.7-g |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{27} \) |
$1.89137$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 5$ |
2B, 5S4 |
$1$ |
\( 2^{2} \) |
$1$ |
$2.400503441$ |
1.814610036 |
\( 28658 a - 19692 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -9 a - 6\) , \( -23 a + 10\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-9a-6\right){x}-23a+10$ |
| 4096.7-g5 |
4096.7-g |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{30} \) |
$1.89137$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 5$ |
2Cs, 5S4 |
$1$ |
\( 2^{4} \) |
$1$ |
$2.400503441$ |
1.814610036 |
\( -924 a + 1784 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 5 a - 7\) , \( 7 a + 3\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(5a-7\right){x}+7a+3$ |
| 4096.7-g6 |
4096.7-g |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{30} \) |
$1.89137$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 5$ |
2Cs, 5S4 |
$1$ |
\( 2^{4} \) |
$1$ |
$2.400503441$ |
1.814610036 |
\( 924 a + 860 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -5 a - 2\) , \( 7 a - 10\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-5a-2\right){x}+7a-10$ |
| 4096.7-h1 |
4096.7-h |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{31} \) |
$1.89137$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.540617835$ |
2.329195233 |
\( 237572 a - 523524 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 43 a - 2\) , \( -23 a - 182\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(43a-2\right){x}-23a-182$ |
| 4096.7-h2 |
4096.7-h |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{22} \) |
$1.89137$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.081235671$ |
2.329195233 |
\( -3084 a - 62716 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 6 a + 3\) , \( a - 9\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(6a+3\right){x}+a-9$ |
| 4096.7-h3 |
4096.7-h |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{26} \) |
$1.89137$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$3.081235671$ |
2.329195233 |
\( -336 a + 560 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 3 a - 2\) , \( a - 6\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(3a-2\right){x}+a-6$ |
| 4096.7-h4 |
4096.7-h |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{25} \) |
$1.89137$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.081235671$ |
2.329195233 |
\( 2056 a + 2768 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( a + 5\) , \( 5 a - 7\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(a+5\right){x}+5a-7$ |
| 4096.7-i1 |
4096.7-i |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{31} \) |
$1.89137$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.540617835$ |
2.329195233 |
\( -237572 a - 285952 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -43 a + 41\) , \( 23 a - 205\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-43a+41\right){x}+23a-205$ |
| 4096.7-i2 |
4096.7-i |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{22} \) |
$1.89137$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.081235671$ |
2.329195233 |
\( 3084 a - 65800 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -6 a + 9\) , \( -a - 8\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-6a+9\right){x}-a-8$ |
| 4096.7-i3 |
4096.7-i |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{26} \) |
$1.89137$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$3.081235671$ |
2.329195233 |
\( 336 a + 224 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -3 a + 1\) , \( -a - 5\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a+1\right){x}-a-5$ |
| 4096.7-i4 |
4096.7-i |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{25} \) |
$1.89137$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.081235671$ |
2.329195233 |
\( -2056 a + 4824 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -a + 6\) , \( -5 a - 2\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-a+6\right){x}-5a-2$ |
*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.
