| 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 |
| 676.4-a1 |
676.4-a |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{7} \cdot 13^{12} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$3.290420844$ |
4.788265656 |
\( -\frac{6735205351063}{308915776} a - \frac{2630717384915}{77228944} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -7 a - 82\) , \( -470 a + 1625\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-7a-82\right){x}-470a+1625$ |
| 676.4-a2 |
676.4-a |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{5} \cdot 13^{8} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$3.290420844$ |
4.788265656 |
\( \frac{322217}{1352} a + \frac{527013}{1352} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -2 a + 8\) , \( 19 a - 51\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a+8\right){x}+19a-51$ |
| 676.4-a3 |
676.4-a |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{7} \cdot 13^{7} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$6.580841688$ |
4.788265656 |
\( -\frac{4036021}{832} a + \frac{12722137}{832} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( -53 a - 83\) , \( 142 a + 221\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-53a-83\right){x}+142a+221$ |
| 676.4-a4 |
676.4-a |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{5} \cdot 13^{9} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$6.580841688$ |
4.788265656 |
\( \frac{35032195942103}{17576} a + \frac{27353536048539}{8788} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( -3858 a - 6043\) , \( 184006 a + 287377\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-3858a-6043\right){x}+184006a+287377$ |
| 676.4-b1 |
676.4-b |
$2$ |
$2$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{9} \cdot 13^{9} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$2.842831880$ |
2.068464020 |
\( -\frac{5010665}{64} a + \frac{12946469}{64} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 567 a - 1454\) , \( 10109 a - 25896\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(567a-1454\right){x}+10109a-25896$ |
| 676.4-b2 |
676.4-b |
$2$ |
$2$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( - 2^{9} \cdot 13^{9} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$2.842831880$ |
2.068464020 |
\( \frac{5924025}{64} a + \frac{2310923}{16} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -201 a - 317\) , \( 1999 a + 3113\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-201a-317\right){x}+1999a+3113$ |
| 676.4-c1 |
676.4-c |
$2$ |
$3$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{24} \cdot 13^{2} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.016663791$ |
$11.19423574$ |
3.257439122 |
\( -\frac{14967538313}{262144} a - \frac{5870975045}{65536} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -20 a - 32\) , \( 80 a + 128\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-20a-32\right){x}+80a+128$ |
| 676.4-c2 |
676.4-c |
$2$ |
$3$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 13^{2} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.049991374$ |
$11.19423574$ |
3.257439122 |
\( \frac{2855}{64} a + \frac{6887}{16} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 3\) , \( 1\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+3{x}+1$ |
| 676.4-d1 |
676.4-d |
$2$ |
$2$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{9} \cdot 13^{3} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{2} \) |
$0.176653796$ |
$20.24130514$ |
1.734470918 |
\( -\frac{5010665}{64} a + \frac{12946469}{64} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -9 a - 14\) , \( 8 a + 12\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-9a-14\right){x}+8a+12$ |
| 676.4-d2 |
676.4-d |
$2$ |
$2$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( - 2^{9} \cdot 13^{3} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{2} \) |
$0.353307593$ |
$10.12065257$ |
1.734470918 |
\( \frac{5924025}{64} a + \frac{2310923}{16} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -3\) , \( -7 a + 13\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}-3{x}-7a+13$ |
| 676.4-e1 |
676.4-e |
$2$ |
$3$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{24} \cdot 13^{8} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.358962073$ |
1.044733091 |
\( -\frac{14967538313}{262144} a - \frac{5870975045}{65536} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 2041 a - 5233\) , \( 161536 a - 413796\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(2041a-5233\right){x}+161536a-413796$ |
| 676.4-e2 |
676.4-e |
$2$ |
$3$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 13^{8} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$3.230658664$ |
1.044733091 |
\( \frac{2855}{64} a + \frac{6887}{16} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 175 a + 274\) , \( -2595 a - 4052\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(175a+274\right){x}-2595a-4052$ |
| 676.4-f1 |
676.4-f |
$1$ |
$1$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 13^{8} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$0.889215470$ |
4.313328599 |
\( \frac{7851401}{1024} a - \frac{20220829}{1024} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( -13 a - 33\) , \( -192 a - 331\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-13a-33\right){x}-192a-331$ |
| 676.4-g1 |
676.4-g |
$8$ |
$12$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( - 2^{4} \cdot 13^{18} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.929576374$ |
0.901821548 |
\( -\frac{118223044620244625}{186384680979848} a + \frac{197298006037352625}{186384680979848} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 195 a - 943\) , \( 3156 a - 1246\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(195a-943\right){x}+3156a-1246$ |
| 676.4-g2 |
676.4-g |
$8$ |
$12$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( - 2^{4} \cdot 13^{10} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.929576374$ |
0.901821548 |
\( -\frac{75681727815625}{228488} a + \frac{24232855929500}{28561} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 260 a - 618\) , \( 2914 a - 7630\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(260a-618\right){x}+2914a-7630$ |
| 676.4-g3 |
676.4-g |
$8$ |
$12$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{13} \cdot 13^{9} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.718305499$ |
0.901821548 |
\( -\frac{13182243091512125}{8998912} a + \frac{33767030646022625}{8998912} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -1636 a - 2617\) , \( 22417 a + 35149\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1636a-2617\right){x}+22417a+35149$ |
| 676.4-g4 |
676.4-g |
$8$ |
$12$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 13^{8} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$3.718305499$ |
0.901821548 |
\( -\frac{85206375}{10816} a + \frac{68689625}{2704} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 10 a - 48\) , \( 26 a - 126\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(10a-48\right){x}+26a-126$ |
| 676.4-g5 |
676.4-g |
$8$ |
$12$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( - 2^{13} \cdot 13^{7} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.718305499$ |
0.901821548 |
\( \frac{166375125}{53248} a + \frac{64966625}{13312} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -31 a + 78\) , \( 4838 a - 12394\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-31a+78\right){x}+4838a-12394$ |
| 676.4-g6 |
676.4-g |
$8$ |
$12$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 13^{12} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$3.718305499$ |
0.901821548 |
\( \frac{94191279954375}{308915776} a + \frac{171323056260125}{308915776} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 25 a - 623\) , \( -538 a + 5946\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(25a-623\right){x}-538a+5946$ |
| 676.4-g7 |
676.4-g |
$8$ |
$12$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{7} \cdot 13^{7} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.718305499$ |
0.901821548 |
\( \frac{991734125}{208} a + \frac{1549202625}{208} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 970 a - 2485\) , \( -13672 a + 35021\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(970a-2485\right){x}-13672a+35021$ |
| 676.4-g8 |
676.4-g |
$8$ |
$12$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( - 2^{7} \cdot 13^{9} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.718305499$ |
0.901821548 |
\( \frac{15192094940649375}{35152} a + \frac{11861629293494125}{17576} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 254 a - 707\) , \( -131173 a + 336189\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(254a-707\right){x}-131173a+336189$ |
| 676.4-h1 |
676.4-h |
$1$ |
$1$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 13^{2} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 5 \) |
$0.015453254$ |
$21.38066475$ |
3.205359110 |
\( \frac{7851401}{1024} a - \frac{20220829}{1024} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 7 a - 15\) , \( -11 a + 27\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(7a-15\right){x}-11a+27$ |
| 676.4-i1 |
676.4-i |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{27} \cdot 13^{6} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.659885177$ |
$3.282920544$ |
3.152503187 |
\( -\frac{55573026649}{16777216} a - \frac{85738862931}{16777216} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -47 a - 50\) , \( 189 a + 504\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-47a-50\right){x}+189a+504$ |
| 676.4-i2 |
676.4-i |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{9} \cdot 13^{6} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$0.247456941$ |
$3.282920544$ |
3.152503187 |
\( -\frac{110887}{256} a + \frac{66933}{64} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( -25 a + 63\) , \( -16 a + 39\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-25a+63\right){x}-16a+39$ |
| 676.4-i3 |
676.4-i |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{27} \cdot 13^{6} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \cdot 3 \) |
$0.082485647$ |
$3.282920544$ |
3.152503187 |
\( \frac{55573026649}{16777216} a - \frac{35327972395}{4194304} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( 345 a - 882\) , \( -5169 a + 13248\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(345a-882\right){x}-5169a+13248$ |
| 676.4-i4 |
676.4-i |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{9} \cdot 13^{6} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1.979655531$ |
$3.282920544$ |
3.152503187 |
\( \frac{110887}{256} a + \frac{156845}{256} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 3 a + 5\) , \( a - 7\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(3a+5\right){x}+a-7$ |
| 676.4-i5 |
676.4-i |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{6} \cdot 13^{6} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$0.989827765$ |
$6.565841088$ |
3.152503187 |
\( -\frac{915957}{16} a + \frac{2374013}{16} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( -319 a - 497\) , \( 124 a + 193\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-319a-497\right){x}+124a+193$ |
| 676.4-i6 |
676.4-i |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{9} \cdot 13^{6} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.329942588$ |
$3.282920544$ |
3.152503187 |
\( -\frac{653762688677050897}{64} a + \frac{418661913522614865}{16} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( 199 a - 1990\) , \( -14489 a + 19668\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(199a-1990\right){x}-14489a+19668$ |
| 676.4-i7 |
676.4-i |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{18} \cdot 13^{6} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \cdot 3 \) |
$0.164971294$ |
$6.565841088$ |
3.152503187 |
\( -\frac{203862548967}{4096} a + \frac{130566616997}{1024} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -81 a - 270\) , \( 743 a + 1812\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-81a-270\right){x}+743a+1812$ |
| 676.4-i8 |
676.4-i |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{6} \cdot 13^{6} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \) |
$0.494913882$ |
$6.565841088$ |
3.152503187 |
\( \frac{915957}{16} a + \frac{182257}{2} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -21 a - 35\) , \( -78 a - 122\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-21a-35\right){x}-78a-122$ |
| 676.4-i9 |
676.4-i |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{3} \cdot 13^{6} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1.979655531$ |
$3.282920544$ |
3.152503187 |
\( -\frac{54503407609}{4} a + \frac{139614751755}{4} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( 2806 a - 7189\) , \( 114963 a - 294484\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(2806a-7189\right){x}+114963a-294484$ |
| 676.4-i10 |
676.4-i |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{18} \cdot 13^{6} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.329942588$ |
$6.565841088$ |
3.152503187 |
\( \frac{203862548967}{4096} a + \frac{318403919021}{4096} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( 956 a - 2464\) , \( -22281 a + 57086\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(956a-2464\right){x}-22281a+57086$ |
| 676.4-i11 |
676.4-i |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{3} \cdot 13^{6} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.989827765$ |
$3.282920544$ |
3.152503187 |
\( \frac{54503407609}{4} a + \frac{42555672073}{2} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -331 a - 545\) , \( -4886 a - 7574\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-331a-545\right){x}-4886a-7574$ |
| 676.4-i12 |
676.4-i |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{9} \cdot 13^{6} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.659885177$ |
$3.282920544$ |
3.152503187 |
\( \frac{653762688677050897}{64} a + \frac{1020884965413408563}{64} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( 2916 a - 7744\) , \( 99831 a - 254210\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(2916a-7744\right){x}+99831a-254210$ |
| 676.4-j1 |
676.4-j |
$2$ |
$2$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( - 2^{24} \cdot 13^{9} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1.231835114$ |
1.792583395 |
\( -\frac{137756047}{262144} a + \frac{91925389}{65536} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 400 a - 1014\) , \( -2827 a + 7189\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(400a-1014\right){x}-2827a+7189$ |
| 676.4-j2 |
676.4-j |
$2$ |
$2$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{21} \cdot 13^{9} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1.231835114$ |
1.792583395 |
\( -\frac{44214665}{4096} a + \frac{177313221}{4096} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -339 a - 609\) , \( -5167 a - 8283\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-339a-609\right){x}-5167a-8283$ |
| 676.4-k1 |
676.4-k |
$4$ |
$14$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{3} \cdot 13^{20} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 7$ |
2B, 7B.6.3 |
$1$ |
\( 2^{3} \) |
$3.567575288$ |
$0.896181439$ |
3.101734516 |
\( \frac{6204347595722997987671}{15749505542797156} a - \frac{9084142193327588424433}{7874752771398578} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 881 a - 12698\) , \( -59247 a + 551857\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(881a-12698\right){x}-59247a+551857$ |
| 676.4-k2 |
676.4-k |
$4$ |
$14$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{21} \cdot 13^{8} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 7$ |
2B, 7B.6.1 |
$1$ |
\( 2^{3} \cdot 7 \) |
$0.509653612$ |
$0.896181439$ |
3.101734516 |
\( -\frac{44029607}{2768896} a + \frac{22287093}{692224} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -9 a + 12\) , \( -15 a - 311\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-9a+12\right){x}-15a-311$ |
| 676.4-k3 |
676.4-k |
$4$ |
$14$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{21} \cdot 13^{7} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 7$ |
2B, 7B.6.1 |
$1$ |
\( 2^{3} \cdot 7 \) |
$0.254826806$ |
$1.792362879$ |
3.101734516 |
\( \frac{5011229819}{212992} a + \frac{11146070857}{212992} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -1996 a - 3119\) , \( -67668 a - 105671\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(-1996a-3119\right){x}-67668a-105671$ |
| 676.4-k4 |
676.4-k |
$4$ |
$14$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{3} \cdot 13^{13} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 7$ |
2B, 7B.6.3 |
$1$ |
\( 2^{3} \) |
$1.783787644$ |
$1.792362879$ |
3.101734516 |
\( -\frac{189319137825824778059}{250994068} a + \frac{490244486042717742153}{250994068} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -407966 a - 638459\) , \( 204219854 a + 318919397\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(-407966a-638459\right){x}+204219854a+318919397$ |
| 676.4-l1 |
676.4-l |
$2$ |
$2$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( - 2^{24} \cdot 13^{3} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{3} \cdot 3^{3} \) |
$0.036803006$ |
$5.940708196$ |
5.726916018 |
\( -\frac{137756047}{262144} a + \frac{91925389}{65536} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 26 a + 42\) , \( 595 a + 929\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(26a+42\right){x}+595a+929$ |
| 676.4-l2 |
676.4-l |
$2$ |
$2$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
676.4 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{21} \cdot 13^{3} \) |
$1.87867$ |
$(-a+2), (-a-1), (-2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{3} \cdot 3^{3} \) |
$0.018401503$ |
$11.88141639$ |
5.726916018 |
\( -\frac{44214665}{4096} a + \frac{177313221}{4096} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( 33 a - 89\) , \( -134 a + 349\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(33a-89\right){x}-134a+349$ |
*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.
