| 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 |
| 7168.7-a1 |
7168.7-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{25} \cdot 7^{4} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.364742336$ |
$1.538008342$ |
3.392468547 |
\( \frac{91484}{49} a - \frac{488028}{49} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 20 a - 24\) , \( 44 a - 4\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(20a-24\right){x}+44a-4$ |
| 7168.7-a2 |
7168.7-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{10} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.458969347$ |
$6.152033368$ |
3.392468547 |
\( -\frac{21696}{7} a - \frac{9088}{7} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+{x}$ |
| 7168.7-a3 |
7168.7-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{20} \cdot 7^{2} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.729484673$ |
$3.076016684$ |
3.392468547 |
\( \frac{3408}{7} a - 1360 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -4\) , \( 4 a + 4\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-4{x}+4a+4$ |
| 7168.7-a4 |
7168.7-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{25} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.458969347$ |
$1.538008342$ |
3.392468547 |
\( -\frac{12673028}{7} a + \frac{25007348}{7} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -20 a - 64\) , \( 140 a + 188\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-20a-64\right){x}+140a+188$ |
| 7168.7-b1 |
7168.7-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{31} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.691848366$ |
2.091952824 |
\( -\frac{4096655365}{28} a - \frac{1660660737}{28} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 171 a - 682\) , \( -2369 a + 6298\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(171a-682\right){x}-2369a+6298$ |
| 7168.7-b2 |
7168.7-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{23} \cdot 7^{2} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.383696732$ |
2.091952824 |
\( \frac{13647889}{14} a - \frac{94721547}{14} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -65 a + 94\) , \( -23 a - 422\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-65a+94\right){x}-23a-422$ |
| 7168.7-b3 |
7168.7-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{32} \cdot 7^{2} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.383696732$ |
2.091952824 |
\( \frac{1145925}{112} a - \frac{1290439}{112} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 11 a - 42\) , \( -33 a + 90\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(11a-42\right){x}-33a+90$ |
| 7168.7-b4 |
7168.7-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{37} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.383696732$ |
2.091952824 |
\( \frac{138325}{1792} a - \frac{774199}{1792} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -4 a + 16\) , \( -36 a - 20\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a+16\right){x}-36a-20$ |
| 7168.7-b5 |
7168.7-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{29} \cdot 7^{8} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.691848366$ |
2.091952824 |
\( \frac{5786513}{4802} a - \frac{2104499}{4802} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -68 a + 16\) , \( 144 a - 368\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-68a+16\right){x}+144a-368$ |
| 7168.7-b6 |
7168.7-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{28} \cdot 7^{4} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.383696732$ |
2.091952824 |
\( -\frac{361845}{196} a + \frac{274391}{196} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 12 a + 16\) , \( 48 a - 48\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(12a+16\right){x}+48a-48$ |
| 7168.7-c1 |
7168.7-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{26} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.815201115$ |
$1.347763164$ |
3.322150588 |
\( \frac{39051258}{7} a - \frac{25340662}{7} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 86 a - 43\) , \( 261 a + 150\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(86a-43\right){x}+261a+150$ |
| 7168.7-c2 |
7168.7-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{17} \cdot 7^{4} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.815201115$ |
$2.695526328$ |
3.322150588 |
\( -\frac{24238}{49} a + \frac{44442}{49} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( a - 6\) , \( 6 a - 4\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(a-6\right){x}+6a-4$ |
| 7168.7-c3 |
7168.7-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{22} \cdot 7^{2} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.407600557$ |
$2.695526328$ |
3.322150588 |
\( \frac{10452}{7} a + \frac{13028}{7} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 6 a - 3\) , \( 5 a - 2\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(6a-3\right){x}+5a-2$ |
| 7168.7-c4 |
7168.7-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{23} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.815201115$ |
$2.695526328$ |
3.322150588 |
\( -\frac{88712}{7} a + \frac{116960}{7} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 4 a - 12\) , \( 4 a - 12\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(4a-12\right){x}+4a-12$ |
| 7168.7-d1 |
7168.7-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{22} \cdot 7^{2} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.839949937$ |
2.146800363 |
\( \frac{432}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -a - 1\) , \( 2 a - 6\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}+2a-6$ |
| 7168.7-d2 |
7168.7-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{28} \cdot 7^{8} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.709987484$ |
2.146800363 |
\( \frac{11090466}{2401} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 59 a + 59\) , \( -138 a + 414\bigr] \) |
${y}^2={x}^{3}+\left(59a+59\right){x}-138a+414$ |
| 7168.7-d3 |
7168.7-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{26} \cdot 7^{4} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.419974968$ |
2.146800363 |
\( \frac{740772}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 19 a + 19\) , \( 30 a - 90\bigr] \) |
${y}^2={x}^{3}+\left(19a+19\right){x}+30a-90$ |
| 7168.7-d4 |
7168.7-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{20} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.839949937$ |
2.146800363 |
\( -\frac{516132}{7} a + \frac{464076}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -a - 13\) , \( -2 a - 18\bigr] \) |
${y}^2={x}^{3}+\left(-a-13\right){x}-2a-18$ |
| 7168.7-d5 |
7168.7-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{20} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.839949937$ |
2.146800363 |
\( \frac{516132}{7} a - \frac{52056}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -10 a + 2\) , \( 13 a - 15\bigr] \) |
${y}^2={x}^{3}+\left(-10a+2\right){x}+13a-15$ |
| 7168.7-d6 |
7168.7-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{28} \cdot 7^{2} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.709987484$ |
2.146800363 |
\( \frac{1443468546}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 299 a + 299\) , \( 1990 a - 5970\bigr] \) |
${y}^2={x}^{3}+\left(299a+299\right){x}+1990a-5970$ |
| 7168.7-e1 |
7168.7-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{27} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.243768276$ |
$2.455176779$ |
3.619352797 |
\( \frac{2525}{7} a + \frac{8121}{7} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4 a - 8\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(4a-8\right){x}$ |
| 7168.7-e2 |
7168.7-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{24} \cdot 7^{2} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.487536553$ |
$2.455176779$ |
3.619352797 |
\( -\frac{3555}{7} a + \frac{15857}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -5 a - 2\) , \( 5 a + 2\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-5a-2\right){x}+5a+2$ |
| 7168.7-e3 |
7168.7-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{27} \cdot 7^{4} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.975073107$ |
$1.227588389$ |
3.619352797 |
\( \frac{1482409}{49} a + \frac{907013}{49} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -45 a - 2\) , \( -131 a + 114\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-45a-2\right){x}-131a+114$ |
| 7168.7-e4 |
7168.7-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{18} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.975073107$ |
$2.455176779$ |
3.619352797 |
\( -\frac{9225207}{7} a + \frac{9710861}{7} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 13 a - 30\) , \( 36 a - 36\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(13a-30\right){x}+36a-36$ |
| 7168.7-f1 |
7168.7-f |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{31} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.691848366$ |
2.091952824 |
\( \frac{4096655365}{28} a - \frac{2878658051}{14} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -468 a + 384\) , \( 2140 a - 7060\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-468a+384\right){x}+2140a-7060$ |
| 7168.7-f2 |
7168.7-f |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{23} \cdot 7^{2} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.383696732$ |
2.091952824 |
\( -\frac{13647889}{14} a - \frac{40536829}{7} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 55 a - 105\) , \( -282 a + 254\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(55a-105\right){x}-282a+254$ |
| 7168.7-f3 |
7168.7-f |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{32} \cdot 7^{2} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.383696732$ |
2.091952824 |
\( -\frac{1145925}{112} a - \frac{72257}{56} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -28 a + 24\) , \( 44 a - 132\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-28a+24\right){x}+44a-132$ |
| 7168.7-f4 |
7168.7-f |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{37} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.383696732$ |
2.091952824 |
\( -\frac{138325}{1792} a - \frac{317937}{896} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 11 a - 10\) , \( -33 a - 6\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(11a-10\right){x}-33a-6$ |
| 7168.7-f5 |
7168.7-f |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{29} \cdot 7^{8} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.691848366$ |
2.091952824 |
\( -\frac{5786513}{4802} a + \frac{263001}{343} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -5 a - 90\) , \( -99 a + 466\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-5a-90\right){x}-99a+466$ |
| 7168.7-f6 |
7168.7-f |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{28} \cdot 7^{4} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.383696732$ |
2.091952824 |
\( \frac{361845}{196} a - \frac{43727}{98} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 15 a + 10\) , \( -3 a + 50\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(15a+10\right){x}-3a+50$ |
| 7168.7-g1 |
7168.7-g |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{26} \cdot 7^{2} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.537774765$ |
$2.261235310$ |
3.676945099 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 0\) , \( -4 a + 12\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}-4a+12$ |
| 7168.7-g2 |
7168.7-g |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{25} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.268887382$ |
$2.261235310$ |
3.676945099 |
\( -\frac{59930}{7} a + \frac{346862}{7} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 14 a - 3\) , \( 13 a + 14\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(14a-3\right){x}+13a+14$ |
| 7168.7-g3 |
7168.7-g |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{25} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.075549531$ |
$2.261235310$ |
3.676945099 |
\( \frac{59930}{7} a + \frac{286932}{7} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 2 a + 17\) , \( -29 a + 18\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(2a+17\right){x}-29a+18$ |
| 7168.7-g4 |
7168.7-g |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{28} \cdot 7^{4} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1.075549531$ |
$1.130617655$ |
3.676945099 |
\( \frac{3543122}{49} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 40 a + 40\) , \( -84 a + 252\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(40a+40\right){x}-84a+252$ |
| 7168.7-h1 |
7168.7-h |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{66} \cdot 7^{2} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$9$ |
\( 2^{5} \) |
$1$ |
$0.154753348$ |
2.105685636 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 2728 a + 2728\) , \( -55920 a + 167760\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(2728a+2728\right){x}-55920a+167760$ |
| 7168.7-h2 |
7168.7-h |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{45} \cdot 7^{3} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.464260044$ |
2.105685636 |
\( -\frac{10538337875}{200704} a - \frac{13018580375}{100352} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 62 a - 579\) , \( -673 a + 5374\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(62a-579\right){x}-673a+5374$ |
| 7168.7-h3 |
7168.7-h |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{45} \cdot 7^{3} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.464260044$ |
2.105685636 |
\( \frac{10538337875}{200704} a - \frac{36575498625}{200704} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -418 a + 221\) , \( -2659 a + 5262\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-418a+221\right){x}-2659a+5262$ |
| 7168.7-h4 |
7168.7-h |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{35} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.392780133$ |
2.105685636 |
\( -\frac{831875}{112} a - \frac{166375}{112} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -18 a - 19\) , \( 45 a + 30\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-18a-19\right){x}+45a+30$ |
| 7168.7-h5 |
7168.7-h |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{35} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.392780133$ |
2.105685636 |
\( \frac{831875}{112} a - \frac{499125}{56} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -18 a - 19\) , \( -49 a - 18\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-18a-19\right){x}-49a-18$ |
| 7168.7-h6 |
7168.7-h |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{34} \cdot 7^{2} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.392780133$ |
2.105685636 |
\( -\frac{15625}{28} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 8 a + 8\) , \( 16 a - 48\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(8a+8\right){x}+16a-48$ |
| 7168.7-h7 |
7168.7-h |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{42} \cdot 7^{6} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3Cs |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$0.464260044$ |
2.105685636 |
\( \frac{9938375}{21952} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -72 a - 72\) , \( -368 a + 1104\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-72a-72\right){x}-368a+1104$ |
| 7168.7-h8 |
7168.7-h |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{75} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{3} \) |
$1$ |
$0.154753348$ |
2.105685636 |
\( -\frac{70135314719125}{481036337152} a + \frac{179276652423375}{240518168576} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -338 a + 1581\) , \( -5105 a + 28590\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-338a+1581\right){x}-5105a+28590$ |
| 7168.7-h9 |
7168.7-h |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{75} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{3} \) |
$1$ |
$0.154753348$ |
2.105685636 |
\( \frac{70135314719125}{481036337152} a + \frac{288417990127625}{481036337152} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 1102 a - 819\) , \( -13811 a + 26238\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(1102a-819\right){x}-13811a+26238$ |
| 7168.7-h10 |
7168.7-h |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{36} \cdot 7^{12} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{6} \cdot 3 \) |
$1$ |
$0.232130022$ |
2.105685636 |
\( \frac{4956477625}{941192} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 568 a + 568\) , \( -4464 a + 13392\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(568a+568\right){x}-4464a+13392$ |
| 7168.7-h11 |
7168.7-h |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{32} \cdot 7^{4} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.696390066$ |
2.105685636 |
\( \frac{128787625}{98} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 168 a + 168\) , \( 784 a - 2352\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(168a+168\right){x}+784a-2352$ |
| 7168.7-h12 |
7168.7-h |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{48} \cdot 7^{4} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{6} \) |
$1$ |
$0.077376674$ |
2.105685636 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 43688 a + 43688\) , \( -3529328 a + 10587984\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(43688a+43688\right){x}-3529328a+10587984$ |
*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.
