| 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 |
| 15488.20-a1 |
15488.20-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{16} \cdot 11^{9} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.440423686$ |
$0.901434118$ |
2.400908571 |
\( \frac{249748466395}{428717762} a + \frac{268677287127}{428717762} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 4 a - 53\) , \( 50 a + 95\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(4a-53\right){x}+50a+95$ |
| 15488.20-a2 |
15488.20-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{10} \cdot 11^{3} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.440423686$ |
$3.605736472$ |
2.400908571 |
\( \frac{36743275}{1936} a + \frac{2964983}{1936} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -a + 7\) , \( -3 a - 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-a+7\right){x}-3a-1$ |
| 15488.20-a3 |
15488.20-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{14} \cdot 11^{6} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.220211843$ |
$1.802868236$ |
2.400908571 |
\( -\frac{67141725}{58564} a + \frac{157233167}{58564} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -6 a + 17\) , \( 12 a + 9\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-6a+17\right){x}+12a+9$ |
| 15488.20-a4 |
15488.20-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{16} \cdot 11^{6} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.440423686$ |
$0.901434118$ |
2.400908571 |
\( -\frac{92394174795}{29282} a + \frac{21793731097}{29282} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -96 a + 247\) , \( 774 a + 643\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-96a+247\right){x}+774a+643$ |
| 15488.20-b1 |
15488.20-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{41} \cdot 11^{2} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.229437542$ |
$0.876401577$ |
2.953992798 |
\( \frac{16131562657}{184549376} a - \frac{8531119419}{184549376} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 14 a - 26\) , \( 60 a - 212\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(14a-26\right){x}+60a-212$ |
| 15488.20-b2 |
15488.20-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{20} \cdot 11^{8} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.557359385$ |
$0.876401577$ |
2.953992798 |
\( \frac{16280859}{937024} a + \frac{1479117671}{937024} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -5 a + 62\) , \( 3 a - 62\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-5a+62\right){x}+3a-62$ |
| 15488.20-b3 |
15488.20-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{13} \cdot 11^{10} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.278679692$ |
$0.876401577$ |
2.953992798 |
\( -\frac{34401807041}{1714871048} a + \frac{3239379833499}{1714871048} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 47 a - 26\) , \( -43 a - 38\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(47a-26\right){x}-43a-38$ |
| 15488.20-b4 |
15488.20-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{19} \cdot 11^{10} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.114718771$ |
$0.438200788$ |
2.953992798 |
\( \frac{320710739562017}{1714871048} a + \frac{130944650574757}{1714871048} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 35 a + 662\) , \( 5075 a - 3358\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(35a+662\right){x}+5075a-3358$ |
| 15488.20-b5 |
15488.20-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{28} \cdot 11^{4} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.114718771$ |
$0.876401577$ |
2.953992798 |
\( -\frac{78156424101}{495616} a + \frac{112033106855}{495616} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 116 a\) , \( -130 a - 782\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+116a{x}-130a-782$ |
| 15488.20-b6 |
15488.20-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{23} \cdot 11^{2} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.229437542$ |
$0.438200788$ |
2.953992798 |
\( -\frac{32518499729401}{704} a + \frac{722188386307}{704} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 1876 a\) , \( -9282 a - 47246\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+1876a{x}-9282a-47246$ |
| 15488.20-c1 |
15488.20-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{54} \cdot 11^{3} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.338242877$ |
1.022750326 |
\( \frac{31504873455125}{519691042816} a + \frac{50524809992625}{259845521408} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 17 a + 209\) , \( 128 a - 3204\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(17a+209\right){x}+128a-3204$ |
| 15488.20-c2 |
15488.20-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{54} \cdot 11^{3} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.338242877$ |
1.022750326 |
\( -\frac{31504873455125}{519691042816} a + \frac{132554493440375}{519691042816} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -148 a - 29\) , \( -567 a - 2768\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-148a-29\right){x}-567a-2768$ |
| 15488.20-c3 |
15488.20-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{42} \cdot 11^{6} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.338242877$ |
1.022750326 |
\( \frac{1133731711875}{959512576} a + \frac{6924008747375}{959512576} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -92 a + 619\) , \( -3344 a + 181\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-92a+619\right){x}-3344a+181$ |
| 15488.20-c4 |
15488.20-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{42} \cdot 11^{6} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.338242877$ |
1.022750326 |
\( -\frac{1133731711875}{959512576} a + \frac{4028870229625}{479756288} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -437 a + 119\) , \( 3199 a - 3493\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-437a+119\right){x}+3199a-3493$ |
| 15488.20-c5 |
15488.20-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{30} \cdot 11^{9} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.169121438$ |
1.022750326 |
\( \frac{915988506230265125}{54875873536} a + \frac{2123510665930979625}{54875873536} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -1372 a + 9579\) , \( -237584 a + 17845\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-1372a+9579\right){x}-237584a+17845$ |
| 15488.20-c6 |
15488.20-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{30} \cdot 11^{9} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.169121438$ |
1.022750326 |
\( -\frac{915988506230265125}{54875873536} a + \frac{1519749586080622375}{27437936768} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -6757 a + 1799\) , \( 217839 a - 268149\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-6757a+1799\right){x}+217839a-268149$ |
| 15488.20-d1 |
15488.20-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{24} \cdot 11^{6} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.033734412$ |
1.562859530 |
\( \frac{46830231}{234256} a + \frac{377324919}{234256} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -32 a + 7\) , \( -26 a + 65\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-32a+7\right){x}-26a+65$ |
| 15488.20-d2 |
15488.20-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{24} \cdot 11^{6} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.033734412$ |
1.562859530 |
\( -\frac{46830231}{234256} a + \frac{212077575}{117128} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -5 a + 46\) , \( 27 a + 42\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-5a+46\right){x}+27a+42$ |
| 15488.20-d3 |
15488.20-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{21} \cdot 11^{9} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.516867206$ |
1.562859530 |
\( \frac{56046918875913}{857435524} a + \frac{9320189138181}{214358881} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 5 a + 416\) , \( -2371 a + 1428\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(5a+416\right){x}-2371a+1428$ |
| 15488.20-d4 |
15488.20-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{21} \cdot 11^{9} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.516867206$ |
1.562859530 |
\( -\frac{56046918875913}{857435524} a + \frac{93327675428637}{857435524} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -292 a - 13\) , \( 2282 a - 1707\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-292a-13\right){x}+2282a-1707$ |
| 15488.20-d5 |
15488.20-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{27} \cdot 11^{3} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.033734412$ |
1.562859530 |
\( \frac{14003310699}{30976} a + \frac{5238465399}{30976} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -23 a + 148\) , \( -429 a + 66\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-23a+148\right){x}-429a+66$ |
| 15488.20-d6 |
15488.20-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{27} \cdot 11^{3} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.033734412$ |
1.562859530 |
\( -\frac{14003310699}{30976} a + \frac{9620888049}{15488} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -104 a + 31\) , \( 364 a - 481\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-104a+31\right){x}+364a-481$ |
| 15488.20-e1 |
15488.20-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{23} \cdot 11^{2} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.208093150$ |
$2.443829262$ |
6.150771644 |
\( -\frac{150031}{2816} a + \frac{4541269}{2816} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 4 a - 8\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(4a-8\right){x}$ |
| 15488.20-e2 |
15488.20-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{16} \cdot 11^{4} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.416186300$ |
$2.443829262$ |
6.150771644 |
\( \frac{119091}{1936} a + \frac{3575519}{1936} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -5 a - 2\) , \( 3 a - 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-5a-2\right){x}+3a-2$ |
| 15488.20-e3 |
15488.20-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{8} \cdot 11^{5} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.832372600$ |
$2.443829262$ |
6.150771644 |
\( -\frac{1085152369}{58564} a + \frac{6871492395}{58564} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 5 a - 19\) , \( -23 a + 35\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(5a-19\right){x}-23a+35$ |
| 15488.20-e4 |
15488.20-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{17} \cdot 11^{5} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.832372600$ |
$1.221914631$ |
6.150771644 |
\( \frac{9255981777}{58564} a + \frac{40892213717}{58564} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -65 a - 22\) , \( 311 a - 134\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-65a-22\right){x}+311a-134$ |
| 15488.20-f1 |
15488.20-f |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{23} \cdot 11^{2} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$2.418339135$ |
$1.737958760$ |
6.354298938 |
\( \frac{34643161}{176} a - \frac{7276683}{176} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -22 a - 22\) , \( 67 a + 11\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-22a-22\right){x}+67a+11$ |
| 15488.20-f2 |
15488.20-f |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{22} \cdot 11^{4} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.209169567$ |
$1.737958760$ |
6.354298938 |
\( \frac{704969}{484} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 10 a - 15\) , \( -4 a - 19\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(10a-15\right){x}-4a-19$ |
| 15488.20-f3 |
15488.20-f |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{20} \cdot 11^{8} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.418339135$ |
$0.868979380$ |
6.354298938 |
\( \frac{59776471}{29282} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -40 a + 55\) , \( 6 a - 33\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-40a+55\right){x}+6a-33$ |
| 15488.20-f4 |
15488.20-f |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{23} \cdot 11^{2} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.418339135$ |
$1.737958760$ |
6.354298938 |
\( -\frac{34643161}{176} a + \frac{13683239}{88} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 16 a + 28\) , \( -29 a + 91\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(16a+28\right){x}-29a+91$ |
*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.
