| 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 |
| 27104.15-a1 |
27104.15-a |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.15 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{27} \cdot 7^{2} \cdot 11^{8} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.899498976$ |
$0.426306339$ |
3.478441361 |
\( -\frac{7516633}{32768} a + \frac{20064501}{229376} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 98 a - 122\) , \( -1036 a - 644\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(98a-122\right){x}-1036a-644$ |
| 27104.15-b1 |
27104.15-b |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.15 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{6} \cdot 7^{3} \cdot 11^{9} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.550819776$ |
1.249141839 |
\( \frac{174212042017}{260876} a - \frac{1008386788027}{260876} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -457 a + 99\) , \( 4218 a - 4787\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-457a+99\right){x}+4218a-4787$ |
| 27104.15-b2 |
27104.15-b |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.15 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{10} \cdot 7 \cdot 11^{7} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.652459329$ |
1.249141839 |
\( \frac{31487}{4928} a + \frac{42843}{4928} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 3 a - 1\) , \( 18 a - 23\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(3a-1\right){x}+18a-23$ |
| 27104.15-b3 |
27104.15-b |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.15 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{9} \cdot 7^{6} \cdot 11^{12} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.275409888$ |
1.249141839 |
\( -\frac{235309145047}{173612978} a + \frac{1422081865755}{1215290846} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -462 a + 179\) , \( 4887 a - 3875\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-462a+179\right){x}+4887a-3875$ |
| 27104.15-b4 |
27104.15-b |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.15 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{11} \cdot 7^{2} \cdot 11^{8} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.826229664$ |
1.249141839 |
\( -\frac{42961631}{968} a + \frac{652825955}{6776} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 88 a - 151\) , \( 513 a - 441\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(88a-151\right){x}+513a-441$ |
| 27104.15-c1 |
27104.15-c |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.15 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{11} \cdot 7^{10} \cdot 11^{9} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.241770580$ |
1.827613803 |
\( -\frac{600483}{19208} a - \frac{10020329}{134456} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -190 a - 105\) , \( -6549 a - 725\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-190a-105\right){x}-6549a-725$ |
| 27104.15-c2 |
27104.15-c |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.15 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{10} \cdot 7^{5} \cdot 11^{9} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$0.483541161$ |
1.827613803 |
\( -\frac{440909339}{21952} a + \frac{329560985}{21952} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -145 a + 385\) , \( -1386 a - 1295\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-145a+385\right){x}-1386a-1295$ |
| 27104.15-d1 |
27104.15-d |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.15 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{13} \cdot 7^{2} \cdot 11^{2} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 5 \) |
$0.187125977$ |
$2.137075969$ |
6.045956454 |
\( \frac{48977017}{224} a + \frac{53352701}{224} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 13 a + 17\) , \( -25 a + 75\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(13a+17\right){x}-25a+75$ |
| 27104.15-e1 |
27104.15-e |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.15 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{8} \cdot 7 \cdot 11^{3} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.526412681$ |
$4.076115991$ |
6.488044864 |
\( \frac{26973}{112} a - \frac{21519}{112} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -a + 2\) , \( a - 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-a+2\right){x}+a-1$ |
| 27104.15-e2 |
27104.15-e |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.15 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{10} \cdot 7^{2} \cdot 11^{3} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.052825363$ |
$2.038057995$ |
6.488044864 |
\( -\frac{1622025}{4} a + \frac{10998693}{28} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 4 a + 32\) , \( 67 a - 45\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(4a+32\right){x}+67a-45$ |
| 27104.15-f1 |
27104.15-f |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.15 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{14} \cdot 7 \cdot 11^{7} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.976801134$ |
$1.140483224$ |
6.736991813 |
\( \frac{13066183}{1232} a - \frac{1583997}{1232} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -43 a + 30\) , \( -77 a + 237\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-43a+30\right){x}-77a+237$ |
| 27104.15-f2 |
27104.15-f |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.15 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{10} \cdot 7^{2} \cdot 11^{8} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.953602268$ |
$1.140483224$ |
6.736991813 |
\( -\frac{257907}{3388} a - \frac{405343}{3388} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -11 a + 18\) , \( 9 a + 79\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-11a+18\right){x}+9a+79$ |
| 27104.15-f3 |
27104.15-f |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.15 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{5} \cdot 7^{4} \cdot 11^{7} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.907204537$ |
$1.140483224$ |
6.736991813 |
\( -\frac{19342401}{1078} a + \frac{5772059}{1078} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -32 a + 66\) , \( 64 a + 147\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-32a+66\right){x}+64a+147$ |
| 27104.15-f4 |
27104.15-f |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.15 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{11} \cdot 7 \cdot 11^{10} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.907204537$ |
$0.570241612$ |
6.736991813 |
\( \frac{29643138941}{204974} a + \frac{69420816985}{204974} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -261 a + 388\) , \( 557 a + 2927\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-261a+388\right){x}+557a+2927$ |
| 27104.15-g1 |
27104.15-g |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.15 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{23} \cdot 7^{6} \cdot 11^{8} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3^{2} \cdot 5 \) |
$0.347498791$ |
$0.141035120$ |
6.668590563 |
\( -\frac{1055665833336017}{1359970304} a - \frac{11765828816445877}{1359970304} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -7272 a - 859\) , \( -316767 a + 210809\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-7272a-859\right){x}-316767a+210809$ |
| 27104.15-g2 |
27104.15-g |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.15 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{34} \cdot 7^{3} \cdot 11^{7} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3^{2} \cdot 5 \) |
$0.173749395$ |
$0.282070241$ |
6.668590563 |
\( \frac{1289149828217033}{578746843136} a - \frac{316147343757171}{578746843136} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -437 a - 109\) , \( -4944 a + 4287\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-437a-109\right){x}-4944a+4287$ |
| 27104.15-g3 |
27104.15-g |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.15 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{13} \cdot 7^{2} \cdot 11^{12} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1.042496373$ |
$0.423105362$ |
6.668590563 |
\( \frac{320285561975}{396829664} a + \frac{253628140467}{396829664} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -187 a + 126\) , \( -131 a - 1331\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-187a+126\right){x}-131a-1331$ |
| 27104.15-g4 |
27104.15-g |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.15 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{14} \cdot 7 \cdot 11^{9} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.521248186$ |
$0.846210724$ |
6.668590563 |
\( -\frac{10743272825}{9540608} a + \frac{20497220099}{9540608} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 48 a - 4\) , \( 24 a - 181\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(48a-4\right){x}+24a-181$ |
| 27104.15-h1 |
27104.15-h |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.15 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{11} \cdot 7^{2} \cdot 11^{2} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.113983648$ |
$3.410957962$ |
7.053605053 |
\( \frac{62273}{56} a + \frac{141285}{56} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 3\) , \( 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+3{x}+1$ |
| 27104.15-h2 |
27104.15-h |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.15 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{17} \cdot 7^{6} \cdot 11^{2} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$0.037994549$ |
$1.136985987$ |
7.053605053 |
\( \frac{1845252601}{175616} a + \frac{1516600445}{175616} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 35 a - 62\) , \( -147 a + 98\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(35a-62\right){x}-147a+98$ |
| 27104.15-i1 |
27104.15-i |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.15 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{26} \cdot 7 \cdot 11^{3} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$0.191669019$ |
$1.397740537$ |
7.290577947 |
\( -\frac{407590651}{1835008} a - \frac{2522215623}{1835008} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 12 a - 24\) , \( -48 a + 32\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(12a-24\right){x}-48a+32$ |
| 27104.15-i2 |
27104.15-i |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.15 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{13} \cdot 7^{2} \cdot 11^{3} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.383338038$ |
$1.397740537$ |
7.290577947 |
\( \frac{3547857603}{3584} a + \frac{2052455449}{512} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 61 a + 27\) , \( 20 a + 335\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(61a+27\right){x}+20a+335$ |
| 27104.15-j1 |
27104.15-j |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.15 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{48} \cdot 7^{2} \cdot 11^{6} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{6} \cdot 3^{2} \) |
$1.065481787$ |
$0.131974098$ |
7.653290664 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 853 a + 6990\) , \( -180013 a + 149453\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(853a+6990\right){x}-180013a+149453$ |
| 27104.15-j2 |
27104.15-j |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.15 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{27} \cdot 7^{3} \cdot 11^{6} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$0.177580297$ |
$0.395922296$ |
7.653290664 |
\( \frac{10538337875}{200704} a - \frac{36575498625}{200704} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -490 a - 154\) , \( -6468 a + 3356\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-490a-154\right){x}-6468a+3356$ |
| 27104.15-j3 |
27104.15-j |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.15 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{27} \cdot 7^{3} \cdot 11^{6} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$0.710321191$ |
$0.395922296$ |
7.653290664 |
\( -\frac{10538337875}{200704} a - \frac{13018580375}{100352} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 378 a - 761\) , \( -5545 a + 6905\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(378a-761\right){x}-5545a+6905$ |
| 27104.15-j4 |
27104.15-j |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.15 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{17} \cdot 7 \cdot 11^{6} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$2.130963575$ |
$1.187766888$ |
7.653290664 |
\( \frac{831875}{112} a - \frac{499125}{56} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -7 a - 46\) , \( -25 a - 103\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-7a-46\right){x}-25a-103$ |
| 27104.15-j5 |
27104.15-j |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.15 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{17} \cdot 7 \cdot 11^{6} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$0.532740893$ |
$1.187766888$ |
7.653290664 |
\( -\frac{831875}{112} a - \frac{166375}{112} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -5 a - 49\) , \( -13 a + 143\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-5a-49\right){x}-13a+143$ |
| 27104.15-j6 |
27104.15-j |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.15 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{16} \cdot 7^{2} \cdot 11^{6} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{6} \) |
$1.065481787$ |
$1.187766888$ |
7.653290664 |
\( -\frac{15625}{28} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 3 a + 20\) , \( 77 a - 49\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3a+20\right){x}+77a-49$ |
| 27104.15-j7 |
27104.15-j |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.15 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{24} \cdot 7^{6} \cdot 11^{6} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3Cs |
$1$ |
\( 2^{6} \cdot 3^{2} \) |
$0.355160595$ |
$0.395922296$ |
7.653290664 |
\( \frac{9938375}{21952} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -22 a - 185\) , \( -1443 a + 1039\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-22a-185\right){x}-1443a+1039$ |
| 27104.15-j8 |
27104.15-j |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.15 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{57} \cdot 7 \cdot 11^{6} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$0.532740893$ |
$0.131974098$ |
7.653290664 |
\( \frac{70135314719125}{481036337152} a + \frac{288417990127625}{481036337152} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 1425 a + 61\) , \( -32373 a + 13575\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(1425a+61\right){x}-32373a+13575$ |
| 27104.15-j9 |
27104.15-j |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.15 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{57} \cdot 7 \cdot 11^{6} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$2.130963575$ |
$0.131974098$ |
7.653290664 |
\( -\frac{70135314719125}{481036337152} a + \frac{179276652423375}{240518168576} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -1187 a + 1894\) , \( -28915 a + 34039\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1187a+1894\right){x}-28915a+34039$ |
| 27104.15-j10 |
27104.15-j |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.15 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{18} \cdot 7^{12} \cdot 11^{6} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$0.710321191$ |
$0.197961148$ |
7.653290664 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 178 a + 1455\) , \( -13363 a + 11711\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(178a+1455\right){x}-13363a+11711$ |
| 27104.15-j11 |
27104.15-j |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.15 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{14} \cdot 7^{4} \cdot 11^{6} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$2.130963575$ |
$0.593883444$ |
7.653290664 |
\( \frac{128787625}{98} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 53 a + 430\) , \( 3117 a - 2225\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(53a+430\right){x}+3117a-2225$ |
| 27104.15-j12 |
27104.15-j |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.15 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{30} \cdot 7^{4} \cdot 11^{6} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$2.130963575$ |
$0.065987049$ |
7.653290664 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 13653 a + 111950\) , \( -11730733 a + 9512909\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(13653a+111950\right){x}-11730733a+9512909$ |
*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.
