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 |
23716.4-a1 |
23716.4-a |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.4 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{18} \cdot 7^{8} \cdot 11^{4} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$0.383868981$ |
0.870533023 |
\( -\frac{14992796757}{32768} a - \frac{10971811273}{32768} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -239 a + 1106\) , \( 8296 a + 1708\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-239a+1106\right){x}+8296a+1708$ |
23716.4-a2 |
23716.4-a |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.4 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{6} \cdot 7^{8} \cdot 11^{4} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$1.151606943$ |
0.870533023 |
\( -\frac{51957}{32} a - \frac{18265}{32} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -29 a + 21\) , \( 43 a - 119\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-29a+21\right){x}+43a-119$ |
23716.4-b1 |
23716.4-b |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.4 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{10} \cdot 7^{6} \cdot 11^{9} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$1.085177090$ |
$0.191554991$ |
2.514172357 |
\( \frac{2775668240489}{85184} a - \frac{3929396676037}{42592} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( 2412 a + 5574\) , \( 151200 a - 230660\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2412a+5574\right){x}+151200a-230660$ |
23716.4-b2 |
23716.4-b |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.4 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{14} \cdot 7^{6} \cdot 11^{12} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{6} \) |
$2.170354180$ |
$0.191554991$ |
2.514172357 |
\( \frac{49453830610989}{7256313856} a - \frac{991801247255}{3628156928} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -1223 a + 1581\) , \( -2906 a - 29970\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-1223a+1581\right){x}-2906a-29970$ |
23716.4-b3 |
23716.4-b |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.4 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{7} \cdot 7^{6} \cdot 11^{18} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$4.340708360$ |
$0.095777495$ |
2.514172357 |
\( -\frac{41728910180660407}{200859416110144} a - \frac{5044929390482523}{100429708055072} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 2067 a + 111\) , \( 29910 a - 161122\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(2067a+111\right){x}+29910a-161122$ |
23716.4-b4 |
23716.4-b |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.4 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{14} \cdot 7^{6} \cdot 11^{7} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$0.361725696$ |
$0.574664973$ |
2.514172357 |
\( \frac{2222449}{45056} a + \frac{42043605}{45056} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( 67 a + 44\) , \( 336 a - 52\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(67a+44\right){x}+336a-52$ |
23716.4-b5 |
23716.4-b |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.4 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{10} \cdot 7^{6} \cdot 11^{8} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{6} \) |
$0.723451393$ |
$0.574664973$ |
2.514172357 |
\( -\frac{998361}{7744} a + \frac{23448551}{7744} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 72 a - 169\) , \( 363 a - 416\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(72a-169\right){x}+363a-416$ |
23716.4-b6 |
23716.4-b |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.4 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{25} \cdot 7^{6} \cdot 11^{9} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$4.340708360$ |
$0.191554991$ |
2.514172357 |
\( -\frac{74168468086089}{22330474496} a + \frac{45400743717419}{11165237248} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -205 a - 1510\) , \( 2006 a + 23450\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-205a-1510\right){x}+2006a+23450$ |
23716.4-b7 |
23716.4-b |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.4 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{11} \cdot 7^{6} \cdot 11^{7} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1.446902786$ |
$0.574664973$ |
2.514172357 |
\( \frac{7153263}{2816} a + \frac{40910099}{1408} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 180 a + 30\) , \( -10 a + 1680\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(180a+30\right){x}-10a+1680$ |
23716.4-b8 |
23716.4-b |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.4 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{5} \cdot 7^{6} \cdot 11^{10} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1.446902786$ |
$0.287332486$ |
2.514172357 |
\( -\frac{67333244623}{117128} a + \frac{557731279327}{117128} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 1052 a - 2409\) , \( 27439 a - 38104\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(1052a-2409\right){x}+27439a-38104$ |
23716.4-c1 |
23716.4-c |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.4 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{9} \cdot 7^{4} \cdot 11^{8} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.786053931$ |
1.188401839 |
\( \frac{1804271}{256} a - \frac{176701}{128} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -85 a + 28\) , \( 246 a - 462\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-85a+28\right){x}+246a-462$ |
23716.4-c2 |
23716.4-c |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.4 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{27} \cdot 7^{4} \cdot 11^{8} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$0.262017977$ |
1.188401839 |
\( -\frac{244445227817}{16777216} a + \frac{189604608459}{8388608} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 265 a + 1043\) , \( 10921 a - 11431\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(265a+1043\right){x}+10921a-11431$ |
23716.4-d1 |
23716.4-d |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.4 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{35} \cdot 7^{8} \cdot 11^{8} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$5.427371109$ |
$0.095007311$ |
4.677445842 |
\( \frac{3249994516225}{8589934592} a - \frac{36175316196699}{8589934592} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -2160 a + 6587\) , \( 127480 a + 80853\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2160a+6587\right){x}+127480a+80853$ |
23716.4-d2 |
23716.4-d |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.4 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{17} \cdot 7^{8} \cdot 11^{8} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{3} \) |
$1.809123703$ |
$0.285021933$ |
4.677445842 |
\( -\frac{89671}{2048} a + \frac{3045277}{2048} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 185 a - 588\) , \( -1159 a - 578\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(185a-588\right){x}-1159a-578$ |
23716.4-e1 |
23716.4-e |
$4$ |
$14$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.4 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{3} \cdot 7^{3} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 7$ |
2B, 7B.6.2[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$2.001846424$ |
3.026507316 |
\( \frac{16471}{4} a - 3375 \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( -9 a - 5\) , \( 13 a - 4\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-9a-5\right){x}+13a-4$ |
23716.4-e2 |
23716.4-e |
$4$ |
$14$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.4 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{3} \cdot 7^{3} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 7$ |
2B, 7B.6.2[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$2.001846424$ |
3.026507316 |
\( -\frac{16471}{4} a + \frac{2971}{4} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -12 a + 6\) , \( 12 a - 22\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-12a+6\right){x}+12a-22$ |
23716.4-e3 |
23716.4-e |
$4$ |
$14$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.4 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{21} \cdot 7^{9} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 7$ |
2B, 7B.6.1[2] |
$1$ |
\( 2^{3} \cdot 7 \) |
$1$ |
$0.285978060$ |
3.026507316 |
\( \frac{1875341}{16384} a + \frac{13640585}{8192} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( 361 a - 505\) , \( -787 a + 1306\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(361a-505\right){x}-787a+1306$ |
23716.4-e4 |
23716.4-e |
$4$ |
$14$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.4 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{21} \cdot 7^{9} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 7$ |
2B, 7B.6.1[2] |
$1$ |
\( 2^{3} \cdot 7 \) |
$1$ |
$0.285978060$ |
3.026507316 |
\( -\frac{1875341}{16384} a + \frac{29156511}{16384} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( 178 a + 436\) , \( -1168 a + 428\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(178a+436\right){x}-1168a+428$ |
23716.4-f1 |
23716.4-f |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.4 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{9} \cdot 7^{10} \cdot 11^{2} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$0.985370750$ |
1.489740546 |
\( \frac{1804271}{256} a - \frac{176701}{128} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -8 a - 67\) , \( -30 a - 201\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(-8a-67\right){x}-30a-201$ |
23716.4-f2 |
23716.4-f |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.4 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{27} \cdot 7^{10} \cdot 11^{2} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$0.328456916$ |
1.489740546 |
\( -\frac{244445227817}{16777216} a + \frac{189604608459}{8388608} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -498 a + 668\) , \( -324 a - 8384\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(-498a+668\right){x}-324a-8384$ |
23716.4-g1 |
23716.4-g |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.4 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{36} \cdot 7^{8} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{6} \cdot 3^{2} \) |
$1$ |
$0.099763041$ |
2.714895745 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -9548 a + 1193\) , \( -415905 a + 422021\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-9548a+1193\right){x}-415905a+422021$ |
23716.4-g2 |
23716.4-g |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.4 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{15} \cdot 7^{9} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.299289124$ |
2.714895745 |
\( \frac{10538337875}{200704} a - \frac{36575498625}{200704} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 835 a - 1164\) , \( -14225 a + 9941\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(835a-1164\right){x}-14225a+9941$ |
23716.4-g3 |
23716.4-g |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.4 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{15} \cdot 7^{9} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.299289124$ |
2.714895745 |
\( -\frac{10538337875}{200704} a - \frac{13018580375}{100352} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 414 a + 1006\) , \( -11079 a + 16329\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(414a+1006\right){x}-11079a+16329$ |
23716.4-g4 |
23716.4-g |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.4 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{5} \cdot 7^{7} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.897867372$ |
2.714895745 |
\( \frac{831875}{112} a - \frac{499125}{56} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 64 a - 9\) , \( -103 a - 289\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(64a-9\right){x}-103a-289$ |
23716.4-g5 |
23716.4-g |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.4 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{5} \cdot 7^{7} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.897867372$ |
2.714895745 |
\( -\frac{831875}{112} a - \frac{166375}{112} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 65 a - 9\) , \( 41 a + 323\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(65a-9\right){x}+41a+323$ |
23716.4-g6 |
23716.4-g |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.4 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{4} \cdot 7^{8} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.897867372$ |
2.714895745 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -28 a + 3\) , \( 119 a - 121\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-28a+3\right){x}+119a-121$ |
23716.4-g7 |
23716.4-g |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.4 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{12} \cdot 7^{12} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3Cs |
$1$ |
\( 2^{6} \cdot 3 \) |
$1$ |
$0.299289124$ |
2.714895745 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 252 a - 32\) , \( -2737 a + 2777\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(252a-32\right){x}-2737a+2777$ |
23716.4-g8 |
23716.4-g |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.4 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{45} \cdot 7^{7} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.099763041$ |
2.714895745 |
\( \frac{70135314719125}{481036337152} a + \frac{288417990127625}{481036337152} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -1965 a + 3421\) , \( -76203 a + 47545\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1965a+3421\right){x}-76203a+47545$ |
23716.4-g9 |
23716.4-g |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.4 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{45} \cdot 7^{7} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.099763041$ |
2.714895745 |
\( -\frac{70135314719125}{481036337152} a + \frac{179276652423375}{240518168576} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -706 a - 3089\) , \( -63187 a + 91873\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-706a-3089\right){x}-63187a+91873$ |
23716.4-g10 |
23716.4-g |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.4 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{6} \cdot 7^{18} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$4$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.149644562$ |
2.714895745 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -1988 a + 248\) , \( -33201 a + 33689\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1988a+248\right){x}-33201a+33689$ |
23716.4-g11 |
23716.4-g |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.4 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{2} \cdot 7^{10} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.448933686$ |
2.714895745 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -588 a + 73\) , \( 5831 a - 5917\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-588a+73\right){x}+5831a-5917$ |
23716.4-g12 |
23716.4-g |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.4 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{18} \cdot 7^{10} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$0.049881520$ |
2.714895745 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -152908 a + 19113\) , \( -26249377 a + 26635397\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-152908a+19113\right){x}-26249377a+26635397$ |
23716.4-h1 |
23716.4-h |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.4 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{18} \cdot 7^{2} \cdot 11^{10} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 3 \cdot 5 \) |
$1$ |
$0.306221512$ |
3.472225579 |
\( -\frac{14992796757}{32768} a - \frac{10971811273}{32768} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 1026 a + 385\) , \( -1559 a + 25303\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(1026a+385\right){x}-1559a+25303$ |
23716.4-h2 |
23716.4-h |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.4 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{6} \cdot 7^{2} \cdot 11^{10} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 5 \) |
$1$ |
$0.918664538$ |
3.472225579 |
\( -\frac{51957}{32} a - \frac{18265}{32} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -4 a + 60\) , \( 173 a - 21\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a+60\right){x}+173a-21$ |
23716.4-i1 |
23716.4-i |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.4 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{35} \cdot 7^{2} \cdot 11^{2} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \cdot 11 \) |
$0.123209096$ |
$0.833685772$ |
10.24943837 |
\( \frac{3249994516225}{8589934592} a - \frac{36175316196699}{8589934592} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -59 a + 13\) , \( -261 a + 315\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-59a+13\right){x}-261a+315$ |
23716.4-i2 |
23716.4-i |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.4 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{17} \cdot 7^{2} \cdot 11^{2} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \cdot 11 \) |
$0.041069698$ |
$2.501057318$ |
10.24943837 |
\( -\frac{89671}{2048} a + \frac{3045277}{2048} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 6 a - 2\) , \( 5 a - 7\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6a-2\right){x}+5a-7$ |
*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.