| 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 |
| 7168.5-a1 |
7168.5-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{25} \cdot 7^{4} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.364742336$ |
$1.538008342$ |
3.392468547 |
\( -\frac{91484}{49} a - \frac{396544}{49} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -18 a - 5\) , \( -63 a + 35\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-18a-5\right){x}-63a+35$ |
| 7168.5-a2 |
7168.5-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{10} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.458969347$ |
$6.152033368$ |
3.392468547 |
\( \frac{21696}{7} a - \frac{30784}{7} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2 a\) , \( a\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+2a{x}+a$ |
| 7168.5-a3 |
7168.5-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{20} \cdot 7^{2} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.729484673$ |
$3.076016684$ |
3.392468547 |
\( -\frac{3408}{7} a - \frac{6112}{7} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2 a - 5\) , \( -3 a + 3\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(2a-5\right){x}-3a+3$ |
| 7168.5-a4 |
7168.5-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{25} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.458969347$ |
$1.538008342$ |
3.392468547 |
\( \frac{12673028}{7} a + \frac{12334320}{7} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 22 a - 85\) , \( -119 a + 243\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(22a-85\right){x}-119a+243$ |
| 7168.5-b1 |
7168.5-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{31} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.691848366$ |
2.091952824 |
\( \frac{4096655365}{28} a - \frac{2878658051}{14} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -171 a - 511\) , \( 2369 a + 3929\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-171a-511\right){x}+2369a+3929$ |
| 7168.5-b2 |
7168.5-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{23} \cdot 7^{2} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.383696732$ |
2.091952824 |
\( -\frac{13647889}{14} a - \frac{40536829}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 65 a + 29\) , \( 23 a - 445\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(65a+29\right){x}+23a-445$ |
| 7168.5-b3 |
7168.5-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{32} \cdot 7^{2} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.383696732$ |
2.091952824 |
\( -\frac{1145925}{112} a - \frac{72257}{56} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -11 a - 31\) , \( 33 a + 57\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-11a-31\right){x}+33a+57$ |
| 7168.5-b4 |
7168.5-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{37} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.383696732$ |
2.091952824 |
\( -\frac{138325}{1792} a - \frac{317937}{896} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 6 a + 11\) , \( 41 a - 45\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(6a+11\right){x}+41a-45$ |
| 7168.5-b5 |
7168.5-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{29} \cdot 7^{8} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.691848366$ |
2.091952824 |
\( -\frac{5786513}{4802} a + \frac{263001}{343} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 70 a - 53\) , \( -213 a - 171\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(70a-53\right){x}-213a-171$ |
| 7168.5-b6 |
7168.5-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{28} \cdot 7^{4} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.383696732$ |
2.091952824 |
\( \frac{361845}{196} a - \frac{43727}{98} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -10 a + 27\) , \( -37 a - 27\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-10a+27\right){x}-37a-27$ |
| 7168.5-c1 |
7168.5-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{26} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.815201115$ |
$1.347763164$ |
3.322150588 |
\( -\frac{39051258}{7} a + \frac{13710596}{7} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -86 a + 43\) , \( -261 a + 411\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-86a+43\right){x}-261a+411$ |
| 7168.5-c2 |
7168.5-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{17} \cdot 7^{4} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.815201115$ |
$2.695526328$ |
3.322150588 |
\( \frac{24238}{49} a + \frac{20204}{49} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -a - 5\) , \( -6 a + 2\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-a-5\right){x}-6a+2$ |
| 7168.5-c3 |
7168.5-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{22} \cdot 7^{2} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.407600557$ |
$2.695526328$ |
3.322150588 |
\( -\frac{10452}{7} a + \frac{23480}{7} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -6 a + 3\) , \( -5 a + 3\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6a+3\right){x}-5a+3$ |
| 7168.5-c4 |
7168.5-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{23} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.815201115$ |
$2.695526328$ |
3.322150588 |
\( \frac{88712}{7} a + \frac{28248}{7} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -4 a - 8\) , \( -4 a - 8\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-4a-8\right){x}-4a-8$ |
| 7168.5-d1 |
7168.5-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{22} \cdot 7^{2} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.839949937$ |
2.146800363 |
\( \frac{432}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( a - 2\) , \( -2 a - 4\bigr] \) |
${y}^2={x}^{3}+\left(a-2\right){x}-2a-4$ |
| 7168.5-d2 |
7168.5-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{28} \cdot 7^{8} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.709987484$ |
2.146800363 |
\( \frac{11090466}{2401} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -59 a + 118\) , \( 138 a + 276\bigr] \) |
${y}^2={x}^{3}+\left(-59a+118\right){x}+138a+276$ |
| 7168.5-d3 |
7168.5-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{26} \cdot 7^{4} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.419974968$ |
2.146800363 |
\( \frac{740772}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -19 a + 38\) , \( -30 a - 60\bigr] \) |
${y}^2={x}^{3}+\left(-19a+38\right){x}-30a-60$ |
| 7168.5-d4 |
7168.5-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{20} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.839949937$ |
2.146800363 |
\( -\frac{516132}{7} a + \frac{464076}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 10 a - 8\) , \( -13 a - 2\bigr] \) |
${y}^2={x}^{3}+\left(10a-8\right){x}-13a-2$ |
| 7168.5-d5 |
7168.5-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{20} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.839949937$ |
2.146800363 |
\( \frac{516132}{7} a - \frac{52056}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( a - 14\) , \( 2 a - 20\bigr] \) |
${y}^2={x}^{3}+\left(a-14\right){x}+2a-20$ |
| 7168.5-d6 |
7168.5-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{28} \cdot 7^{2} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.709987484$ |
2.146800363 |
\( \frac{1443468546}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -299 a + 598\) , \( -1990 a - 3980\bigr] \) |
${y}^2={x}^{3}+\left(-299a+598\right){x}-1990a-3980$ |
| 7168.5-e1 |
7168.5-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{27} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.243768276$ |
$2.455176779$ |
3.619352797 |
\( -\frac{2525}{7} a + \frac{10646}{7} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -2 a - 5\) , \( 3 a + 5\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a-5\right){x}+3a+5$ |
| 7168.5-e2 |
7168.5-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{24} \cdot 7^{2} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.487536553$ |
$2.455176779$ |
3.619352797 |
\( \frac{3555}{7} a + \frac{12302}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 5 a - 7\) , \( -5 a + 7\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(5a-7\right){x}-5a+7$ |
| 7168.5-e3 |
7168.5-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{27} \cdot 7^{4} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.975073107$ |
$1.227588389$ |
3.619352797 |
\( -\frac{1482409}{49} a + \frac{341346}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 45 a - 47\) , \( 131 a - 17\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(45a-47\right){x}+131a-17$ |
| 7168.5-e4 |
7168.5-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{18} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.975073107$ |
$2.455176779$ |
3.619352797 |
\( \frac{9225207}{7} a + \frac{485654}{7} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -11 a - 18\) , \( -48 a - 18\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-11a-18\right){x}-48a-18$ |
| 7168.5-f1 |
7168.5-f |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{31} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.691848366$ |
2.091952824 |
\( -\frac{4096655365}{28} a - \frac{1660660737}{28} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 470 a - 85\) , \( -1671 a - 5005\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(470a-85\right){x}-1671a-5005$ |
| 7168.5-f2 |
7168.5-f |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{23} \cdot 7^{2} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.383696732$ |
2.091952824 |
\( \frac{13647889}{14} a - \frac{94721547}{14} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -53 a - 51\) , \( 336 a + 23\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-53a-51\right){x}+336a+23$ |
| 7168.5-f3 |
7168.5-f |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{32} \cdot 7^{2} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.383696732$ |
2.091952824 |
\( \frac{1145925}{112} a - \frac{1290439}{112} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 30 a - 5\) , \( -15 a - 93\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(30a-5\right){x}-15a-93$ |
| 7168.5-f4 |
7168.5-f |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{37} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.383696732$ |
2.091952824 |
\( \frac{138325}{1792} a - \frac{774199}{1792} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -11 a + 1\) , \( 33 a - 39\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-11a+1\right){x}+33a-39$ |
| 7168.5-f5 |
7168.5-f |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{29} \cdot 7^{8} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.691848366$ |
2.091952824 |
\( \frac{5786513}{4802} a - \frac{2104499}{4802} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 5 a - 95\) , \( 99 a + 367\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(5a-95\right){x}+99a+367$ |
| 7168.5-f6 |
7168.5-f |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{28} \cdot 7^{4} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.383696732$ |
2.091952824 |
\( -\frac{361845}{196} a + \frac{274391}{196} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -15 a + 25\) , \( 3 a + 47\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-15a+25\right){x}+3a+47$ |
| 7168.5-g1 |
7168.5-g |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{26} \cdot 7^{2} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.537774765$ |
$2.261235310$ |
3.676945099 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 0\) , \( 4 a + 8\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+4a+8$ |
| 7168.5-g2 |
7168.5-g |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{25} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.075549531$ |
$2.261235310$ |
3.676945099 |
\( -\frac{59930}{7} a + \frac{346862}{7} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -2 a + 19\) , \( 29 a - 11\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a+19\right){x}+29a-11$ |
| 7168.5-g3 |
7168.5-g |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{25} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.268887382$ |
$2.261235310$ |
3.676945099 |
\( \frac{59930}{7} a + \frac{286932}{7} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -14 a + 11\) , \( -13 a + 27\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-14a+11\right){x}-13a+27$ |
| 7168.5-g4 |
7168.5-g |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{28} \cdot 7^{4} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1.075549531$ |
$1.130617655$ |
3.676945099 |
\( \frac{3543122}{49} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -40 a + 80\) , \( 84 a + 168\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-40a+80\right){x}+84a+168$ |
| 7168.5-h1 |
7168.5-h |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{66} \cdot 7^{2} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
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 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -2728 a + 5456\) , \( 55920 a + 111840\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-2728a+5456\right){x}+55920a+111840$ |
| 7168.5-h2 |
7168.5-h |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{45} \cdot 7^{3} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.464260044$ |
2.105685636 |
\( -\frac{10538337875}{200704} a - \frac{13018580375}{100352} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 418 a - 197\) , \( 2659 a + 2603\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(418a-197\right){x}+2659a+2603$ |
| 7168.5-h3 |
7168.5-h |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{45} \cdot 7^{3} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.464260044$ |
2.105685636 |
\( \frac{10538337875}{200704} a - \frac{36575498625}{200704} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -62 a - 517\) , \( 673 a + 4701\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-62a-517\right){x}+673a+4701$ |
| 7168.5-h4 |
7168.5-h |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{35} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.392780133$ |
2.105685636 |
\( -\frac{831875}{112} a - \frac{166375}{112} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 18 a - 37\) , \( 49 a - 67\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(18a-37\right){x}+49a-67$ |
| 7168.5-h5 |
7168.5-h |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{35} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.392780133$ |
2.105685636 |
\( \frac{831875}{112} a - \frac{499125}{56} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 18 a - 37\) , \( -45 a + 75\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(18a-37\right){x}-45a+75$ |
| 7168.5-h6 |
7168.5-h |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{34} \cdot 7^{2} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
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 |
\( -\frac{15625}{28} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -8 a + 16\) , \( -16 a - 32\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-8a+16\right){x}-16a-32$ |
| 7168.5-h7 |
7168.5-h |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{42} \cdot 7^{6} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
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 |
\( \frac{9938375}{21952} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 72 a - 144\) , \( 368 a + 736\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(72a-144\right){x}+368a+736$ |
| 7168.5-h8 |
7168.5-h |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{75} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{3} \) |
$1$ |
$0.154753348$ |
2.105685636 |
\( -\frac{70135314719125}{481036337152} a + \frac{179276652423375}{240518168576} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -1102 a + 283\) , \( 13811 a + 12427\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1102a+283\right){x}+13811a+12427$ |
| 7168.5-h9 |
7168.5-h |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{75} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{3} \) |
$1$ |
$0.154753348$ |
2.105685636 |
\( \frac{70135314719125}{481036337152} a + \frac{288417990127625}{481036337152} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 338 a + 1243\) , \( 5105 a + 23485\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(338a+1243\right){x}+5105a+23485$ |
| 7168.5-h10 |
7168.5-h |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{36} \cdot 7^{12} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{6} \cdot 3 \) |
$1$ |
$0.232130022$ |
2.105685636 |
\( \frac{4956477625}{941192} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -568 a + 1136\) , \( 4464 a + 8928\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-568a+1136\right){x}+4464a+8928$ |
| 7168.5-h11 |
7168.5-h |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{32} \cdot 7^{4} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.696390066$ |
2.105685636 |
\( \frac{128787625}{98} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -168 a + 336\) , \( -784 a - 1568\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-168a+336\right){x}-784a-1568$ |
| 7168.5-h12 |
7168.5-h |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{48} \cdot 7^{4} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{6} \) |
$1$ |
$0.077376674$ |
2.105685636 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -43688 a + 87376\) , \( 3529328 a + 7058656\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-43688a+87376\right){x}+3529328a+7058656$ |
*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.
