| 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 |
| 28672.7-a1 |
28672.7-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{26} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.393477166$ |
$2.008147859$ |
4.230644320 |
\( \frac{516132}{7} a - \frac{52056}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 12 a + 16\) , \( -24 a + 56\bigr] \) |
${y}^2={x}^{3}+\left(12a+16\right){x}-24a+56$ |
| 28672.7-a2 |
28672.7-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{28} \cdot 7^{2} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.696738583$ |
$2.008147859$ |
4.230644320 |
\( \frac{432}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4\) , \( 16\bigr] \) |
${y}^2={x}^{3}+4{x}+16$ |
| 28672.7-a3 |
28672.7-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{34} \cdot 7^{8} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.696738583$ |
$0.502036964$ |
4.230644320 |
\( \frac{11090466}{2401} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -236\) , \( -1104\bigr] \) |
${y}^2={x}^{3}-236{x}-1104$ |
| 28672.7-a4 |
28672.7-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{32} \cdot 7^{4} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.393477166$ |
$1.004073929$ |
4.230644320 |
\( \frac{740772}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -76\) , \( 240\bigr] \) |
${y}^2={x}^{3}-76{x}+240$ |
| 28672.7-a5 |
28672.7-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{26} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.393477166$ |
$2.008147859$ |
4.230644320 |
\( -\frac{516132}{7} a + \frac{464076}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -12 a + 28\) , \( 24 a + 32\bigr] \) |
${y}^2={x}^{3}+\left(-12a+28\right){x}+24a+32$ |
| 28672.7-a6 |
28672.7-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{34} \cdot 7^{2} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$2.786954333$ |
$0.502036964$ |
4.230644320 |
\( \frac{1443468546}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1196\) , \( 15920\bigr] \) |
${y}^2={x}^{3}-1196{x}+15920$ |
| 28672.7-b1 |
28672.7-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{23} \cdot 7^{4} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.361504906$ |
$1.906024945$ |
3.923365441 |
\( \frac{24238}{49} a + \frac{20204}{49} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 7 a + 2\) , \( 7 a + 4\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(7a+2\right){x}+7a+4$ |
| 28672.7-b2 |
28672.7-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{28} \cdot 7^{2} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.680752453$ |
$1.906024945$ |
3.923365441 |
\( -\frac{10452}{7} a + \frac{23480}{7} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 9 a - 15\) , \( 13 a + 1\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(9a-15\right){x}+13a+1$ |
| 28672.7-b3 |
28672.7-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{29} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.340376226$ |
$1.906024945$ |
3.923365441 |
\( \frac{88712}{7} a + \frac{28248}{7} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 16 a - 1\) , \( 16 a + 31\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(16a-1\right){x}+16a+31$ |
| 28672.7-b4 |
28672.7-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{32} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.361504906$ |
$0.953012472$ |
3.923365441 |
\( -\frac{39051258}{7} a + \frac{13710596}{7} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 129 a - 215\) , \( 933 a - 711\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(129a-215\right){x}+933a-711$ |
| 28672.7-c1 |
28672.7-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{32} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.361504906$ |
$0.953012472$ |
3.923365441 |
\( \frac{39051258}{7} a - \frac{25340662}{7} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -127 a - 87\) , \( -1061 a + 135\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-127a-87\right){x}-1061a+135$ |
| 28672.7-c2 |
28672.7-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{23} \cdot 7^{4} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.361504906$ |
$1.906024945$ |
3.923365441 |
\( -\frac{24238}{49} a + \frac{44442}{49} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -7 a + 9\) , \( -7 a + 11\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-7a+9\right){x}-7a+11$ |
| 28672.7-c3 |
28672.7-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{28} \cdot 7^{2} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.680752453$ |
$1.906024945$ |
3.923365441 |
\( \frac{10452}{7} a + \frac{13028}{7} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -7 a - 7\) , \( -21 a + 7\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-7a-7\right){x}-21a+7$ |
| 28672.7-c4 |
28672.7-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{29} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.340376226$ |
$1.906024945$ |
3.923365441 |
\( -\frac{88712}{7} a + \frac{116960}{7} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -16 a + 15\) , \( -16 a + 47\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-16a+15\right){x}-16a+47$ |
| 28672.7-d1 |
28672.7-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{32} \cdot 7^{2} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.844493815$ |
$1.598934821$ |
4.082894903 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -1\) , \( 33\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-{x}+33$ |
| 28672.7-d2 |
28672.7-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{31} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.422246907$ |
$1.598934821$ |
4.082894903 |
\( \frac{59930}{7} a + \frac{286932}{7} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 17 a - 39\) , \( -53 a + 55\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(17a-39\right){x}-53a+55$ |
| 28672.7-d3 |
28672.7-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{31} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.422246907$ |
$1.598934821$ |
4.082894903 |
\( -\frac{59930}{7} a + \frac{346862}{7} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -15 a - 23\) , \( 69 a + 25\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-15a-23\right){x}+69a+25$ |
| 28672.7-d4 |
28672.7-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{34} \cdot 7^{4} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.688987630$ |
$0.799467410$ |
4.082894903 |
\( \frac{3543122}{49} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -161\) , \( 833\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-161{x}+833$ |
| 28672.7-e1 |
28672.7-e |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{72} \cdot 7^{2} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \) |
$12.63051067$ |
$0.109427141$ |
4.179140127 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -10913\) , \( 436447\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-10913{x}+436447$ |
| 28672.7-e2 |
28672.7-e |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{51} \cdot 7^{3} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{4} \) |
$2.105085112$ |
$0.328281425$ |
4.179140127 |
\( \frac{10538337875}{200704} a - \frac{36575498625}{200704} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 641 a + 393\) , \( -3355 a + 15449\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(641a+393\right){x}-3355a+15449$ |
| 28672.7-e3 |
28672.7-e |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{51} \cdot 7^{3} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{4} \) |
$2.105085112$ |
$0.328281425$ |
4.179140127 |
\( -\frac{10538337875}{200704} a - \frac{13018580375}{100352} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -639 a + 1033\) , \( 2715 a + 13127\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-639a+1033\right){x}+2715a+13127$ |
| 28672.7-e4 |
28672.7-e |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{41} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.701695037$ |
$0.984844277$ |
4.179140127 |
\( \frac{831875}{112} a - \frac{499125}{56} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 73\) , \( -165 a + 135\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+73\right){x}-165a+135$ |
| 28672.7-e5 |
28672.7-e |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{41} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.701695037$ |
$0.984844277$ |
4.179140127 |
\( -\frac{831875}{112} a - \frac{166375}{112} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 73\) , \( 165 a - 103\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+73\right){x}+165a-103$ |
| 28672.7-e6 |
28672.7-e |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{40} \cdot 7^{2} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \) |
$1.403390075$ |
$0.984844277$ |
4.179140127 |
\( -\frac{15625}{28} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -33\) , \( -161\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-33{x}-161$ |
| 28672.7-e7 |
28672.7-e |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{48} \cdot 7^{6} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3Cs |
$1$ |
\( 2^{5} \) |
$4.210170225$ |
$0.328281425$ |
4.179140127 |
\( \frac{9938375}{21952} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 287\) , \( 3231\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+287{x}+3231$ |
| 28672.7-e8 |
28672.7-e |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{81} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$6.315255337$ |
$0.109427141$ |
4.179140127 |
\( \frac{70135314719125}{481036337152} a + \frac{288417990127625}{481036337152} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -1919 a - 567\) , \( -13275 a + 80665\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1919a-567\right){x}-13275a+80665$ |
| 28672.7-e9 |
28672.7-e |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{81} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$6.315255337$ |
$0.109427141$ |
4.179140127 |
\( -\frac{70135314719125}{481036337152} a + \frac{179276652423375}{240518168576} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 1921 a - 2487\) , \( 15195 a + 64903\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(1921a-2487\right){x}+15195a+64903$ |
| 28672.7-e10 |
28672.7-e |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{42} \cdot 7^{12} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \) |
$8.420340450$ |
$0.164140712$ |
4.179140127 |
\( \frac{4956477625}{941192} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -2273\) , \( 33439\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-2273{x}+33439$ |
| 28672.7-e11 |
28672.7-e |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{38} \cdot 7^{4} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$2.806780150$ |
$0.492422138$ |
4.179140127 |
\( \frac{128787625}{98} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -673\) , \( -6945\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-673{x}-6945$ |
| 28672.7-e12 |
28672.7-e |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{54} \cdot 7^{4} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$25.26102135$ |
$0.054713570$ |
4.179140127 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -174753\) , \( 28059871\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-174753{x}+28059871$ |
| 28672.7-f1 |
28672.7-f |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{21} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.324661931$ |
$2.495279627$ |
4.997297996 |
\( \frac{1111000}{7} a - \frac{1378000}{7} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 16 a - 12\) , \( 30 a - 10\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(16a-12\right){x}+30a-10$ |
| 28672.7-f2 |
28672.7-f |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{21} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.324661931$ |
$2.495279627$ |
4.997297996 |
\( -\frac{1111000}{7} a - \frac{267000}{7} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -14 a + 3\) , \( -15 a + 17\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-14a+3\right){x}-15a+17$ |
| 28672.7-f3 |
28672.7-f |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{24} \cdot 7^{2} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.662330965$ |
$2.495279627$ |
4.997297996 |
\( \frac{8000}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 7\) , \( -7\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+7{x}-7$ |
| 28672.7-f4 |
28672.7-f |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{30} \cdot 7^{4} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.324661931$ |
$1.247639813$ |
4.997297996 |
\( \frac{125000}{49} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -33\) , \( -31\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-33{x}-31$ |
| 28672.7-g1 |
28672.7-g |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{31} \cdot 7^{4} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.333489098$ |
$1.087536128$ |
4.385045760 |
\( \frac{91484}{49} a - \frac{488028}{49} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -43 a + 9\) , \( -119 a + 173\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-43a+9\right){x}-119a+173$ |
| 28672.7-g2 |
28672.7-g |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{26} \cdot 7^{2} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.666744549$ |
$2.175072256$ |
4.385045760 |
\( \frac{3408}{7} a - 1360 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -3 a + 9\) , \( -7 a - 3\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-3a+9\right){x}-7a-3$ |
| 28672.7-g3 |
28672.7-g |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{16} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.333489098$ |
$4.350144512$ |
4.385045760 |
\( -\frac{21696}{7} a - \frac{9088}{7} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 2 a - 1\) , \( -a - 3\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(2a-1\right){x}-a-3$ |
| 28672.7-g4 |
28672.7-g |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{31} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.333489098$ |
$1.087536128$ |
4.385045760 |
\( -\frac{12673028}{7} a + \frac{25007348}{7} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -43 a + 169\) , \( -439 a - 179\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-43a+169\right){x}-439a-179$ |
| 28672.7-h1 |
28672.7-h |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{37} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.489210671$ |
1.479234028 |
\( -\frac{4096655365}{28} a - \frac{1660660737}{28} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -853 a + 1022\) , \( 809 a - 17334\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-853a+1022\right){x}+809a-17334$ |
| 28672.7-h2 |
28672.7-h |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{29} \cdot 7^{2} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.978421342$ |
1.479234028 |
\( \frac{13647889}{14} a - \frac{94721547}{14} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 159 a - 58\) , \( 491 a + 798\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(159a-58\right){x}+491a+798$ |
| 28672.7-h3 |
28672.7-h |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{38} \cdot 7^{2} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.978421342$ |
1.479234028 |
\( \frac{1145925}{112} a - \frac{1290439}{112} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -53 a + 62\) , \( 9 a - 246\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-53a+62\right){x}+9a-246$ |
| 28672.7-h4 |
28672.7-h |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{35} \cdot 7^{8} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.489210671$ |
1.479234028 |
\( \frac{5786513}{4802} a - \frac{2104499}{4802} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 85 a + 105\) , \( -169 a + 1299\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(85a+105\right){x}-169a+1299$ |
| 28672.7-h5 |
28672.7-h |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{43} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.978421342$ |
1.479234028 |
\( \frac{138325}{1792} a - \frac{774199}{1792} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 21 a - 23\) , \( 105 a - 51\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(21a-23\right){x}+105a-51$ |
| 28672.7-h6 |
28672.7-h |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{34} \cdot 7^{4} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.978421342$ |
1.479234028 |
\( -\frac{361845}{196} a + \frac{274391}{196} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 5 a - 55\) , \( -41 a + 147\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(5a-55\right){x}-41a+147$ |
| 28672.7-i1 |
28672.7-i |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{31} \cdot 7^{4} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.333489098$ |
$1.087536128$ |
4.385045760 |
\( -\frac{91484}{49} a - \frac{396544}{49} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 43 a - 34\) , \( 119 a + 54\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(43a-34\right){x}+119a+54$ |
| 28672.7-i2 |
28672.7-i |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{16} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.333489098$ |
$4.350144512$ |
4.385045760 |
\( \frac{21696}{7} a - \frac{30784}{7} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -2 a + 1\) , \( a - 4\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-2a+1\right){x}+a-4$ |
| 28672.7-i3 |
28672.7-i |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{26} \cdot 7^{2} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.666744549$ |
$2.175072256$ |
4.385045760 |
\( -\frac{3408}{7} a - \frac{6112}{7} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 3 a + 6\) , \( 7 a - 10\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(3a+6\right){x}+7a-10$ |
| 28672.7-i4 |
28672.7-i |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{31} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.333489098$ |
$1.087536128$ |
4.385045760 |
\( \frac{12673028}{7} a + \frac{12334320}{7} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 43 a + 126\) , \( 439 a - 618\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(43a+126\right){x}+439a-618$ |
| 28672.7-j1 |
28672.7-j |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{33} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.736072149$ |
2.624694380 |
\( -\frac{2525}{7} a + \frac{10646}{7} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 11 a - 2\) , \( -9 a + 22\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(11a-2\right){x}-9a+22$ |
| 28672.7-j2 |
28672.7-j |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{30} \cdot 7^{2} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.736072149$ |
2.624694380 |
\( \frac{3555}{7} a + \frac{12302}{7} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -3 a + 17\) , \( -17 a + 11\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a+17\right){x}-17a+11$ |
*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.
