| 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 |
| 79.1-a1 |
79.1-a |
$2$ |
$2$ |
\(\Q(\zeta_{13})^+\) |
$6$ |
$[6, 0]$ |
79.1 |
\( 79 \) |
\( - 79^{2} \) |
$78.36687$ |
$(a^3-a^2-2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.038527218$ |
$13265.04999$ |
2.51617 |
\( \frac{1061663819573662758610}{6241} a^{5} - \frac{2267851397132794939683}{6241} a^{4} - \frac{2731746238796018458192}{6241} a^{3} + \frac{7350272748843635563380}{6241} a^{2} - \frac{1980878737512083984999}{6241} a - \frac{934456702058730400830}{6241} \) |
\( \bigl[a^{4} - 4 a^{2} + a + 3\) , \( a^{3} + a^{2} - 4 a - 3\) , \( a^{5} - 5 a^{3} + 5 a + 1\) , \( -4 a^{5} - 4 a^{4} + 11 a^{3} + 9 a^{2} + 4 a - 9\) , \( -5 a^{5} - 12 a^{4} + 28 a^{3} + 22 a^{2} - 34 a + 4\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a+3\right){x}{y}+\left(a^{5}-5a^{3}+5a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-3\right){x}^{2}+\left(-4a^{5}-4a^{4}+11a^{3}+9a^{2}+4a-9\right){x}-5a^{5}-12a^{4}+28a^{3}+22a^{2}-34a+4$ |
| 79.1-a2 |
79.1-a |
$2$ |
$2$ |
\(\Q(\zeta_{13})^+\) |
$6$ |
$[6, 0]$ |
79.1 |
\( 79 \) |
\( -79 \) |
$78.36687$ |
$(a^3-a^2-2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.019263609$ |
$53060.19998$ |
2.51617 |
\( \frac{11177485547}{79} a^{5} - \frac{23876631104}{79} a^{4} - \frac{28760555737}{79} a^{3} + \frac{77385951919}{79} a^{2} - \frac{20855199087}{79} a - \frac{9838223470}{79} \) |
\( \bigl[a^{4} - 4 a^{2} + a + 3\) , \( a^{3} + a^{2} - 4 a - 3\) , \( a^{5} - 5 a^{3} + 5 a + 1\) , \( a^{5} + a^{4} - 4 a^{3} - a^{2} + 4 a + 1\) , \( a^{5} + 2 a^{4} - a^{3} - 5 a^{2} - 3 a\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a+3\right){x}{y}+\left(a^{5}-5a^{3}+5a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-3\right){x}^{2}+\left(a^{5}+a^{4}-4a^{3}-a^{2}+4a+1\right){x}+a^{5}+2a^{4}-a^{3}-5a^{2}-3a$ |
| 79.1-b1 |
79.1-b |
$1$ |
$1$ |
\(\Q(\zeta_{13})^+\) |
$6$ |
$[6, 0]$ |
79.1 |
\( 79 \) |
\( 79^{2} \) |
$78.36687$ |
$(a^3-a^2-2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.001171369$ |
$107610.2235$ |
2.48239 |
\( \frac{10278832194}{6241} a^{5} - \frac{29929897535}{6241} a^{4} + \frac{238271915}{6241} a^{3} + \frac{45269862214}{6241} a^{2} - \frac{15374036487}{6241} a - \frac{6225749444}{6241} \) |
\( \bigl[a^{4} - 4 a^{2} + 2\) , \( a^{5} - 6 a^{3} + 9 a + 1\) , \( a^{4} + a^{3} - 4 a^{2} - 3 a + 3\) , \( 9 a^{5} - 40 a^{3} - 5 a^{2} + 31 a + 3\) , \( -7 a^{5} - 5 a^{4} + 28 a^{3} + 22 a^{2} - 11 a - 5\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+2\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-3a+3\right){y}={x}^{3}+\left(a^{5}-6a^{3}+9a+1\right){x}^{2}+\left(9a^{5}-40a^{3}-5a^{2}+31a+3\right){x}-7a^{5}-5a^{4}+28a^{3}+22a^{2}-11a-5$ |
| 79.1-c1 |
79.1-c |
$4$ |
$10$ |
\(\Q(\zeta_{13})^+\) |
$6$ |
$[6, 0]$ |
79.1 |
\( 79 \) |
\( - 79^{5} \) |
$78.36687$ |
$(a^3-a^2-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$625$ |
\( 1 \) |
$1$ |
$5.837580137$ |
1.49691 |
\( \frac{55023306124512922647620}{3077056399} a^{5} - \frac{118530438657502667153870}{3077056399} a^{4} - \frac{141076757522153256512802}{3077056399} a^{3} + \frac{384280328755279198355509}{3077056399} a^{2} - \frac{104160003334531508958775}{3077056399} a - \frac{48974567195018206908192}{3077056399} \) |
\( \bigl[a^{4} - 3 a^{2} + a\) , \( -a^{4} + 3 a^{2} + a - 1\) , \( a^{4} - 3 a^{2} + a\) , \( -36 a^{5} + 65 a^{4} + 103 a^{3} - 230 a^{2} + 50 a + 24\) , \( -259 a^{5} + 514 a^{4} + 687 a^{3} - 1743 a^{2} + 502 a + 177\bigr] \) |
${y}^2+\left(a^{4}-3a^{2}+a\right){x}{y}+\left(a^{4}-3a^{2}+a\right){y}={x}^{3}+\left(-a^{4}+3a^{2}+a-1\right){x}^{2}+\left(-36a^{5}+65a^{4}+103a^{3}-230a^{2}+50a+24\right){x}-259a^{5}+514a^{4}+687a^{3}-1743a^{2}+502a+177$ |
| 79.1-c2 |
79.1-c |
$4$ |
$10$ |
\(\Q(\zeta_{13})^+\) |
$6$ |
$[6, 0]$ |
79.1 |
\( 79 \) |
\( -79 \) |
$78.36687$ |
$(a^3-a^2-2a+3)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$91212.18964$ |
1.49691 |
\( \frac{12273524}{79} a^{5} - \frac{3709875}{79} a^{4} - \frac{63845719}{79} a^{3} + \frac{4394312}{79} a^{2} + \frac{76199147}{79} a + \frac{16823747}{79} \) |
\( \bigl[a^{5} - 4 a^{3} + 3 a + 1\) , \( a^{5} + a^{4} - 4 a^{3} - 3 a^{2} + a - 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -12 a^{5} + 3 a^{4} + 61 a^{3} - 66 a - 15\) , \( 37 a^{5} - 7 a^{4} - 188 a^{3} + a^{2} + 217 a + 50\bigr] \) |
${y}^2+\left(a^{5}-4a^{3}+3a+1\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{5}+a^{4}-4a^{3}-3a^{2}+a-1\right){x}^{2}+\left(-12a^{5}+3a^{4}+61a^{3}-66a-15\right){x}+37a^{5}-7a^{4}-188a^{3}+a^{2}+217a+50$ |
| 79.1-c3 |
79.1-c |
$4$ |
$10$ |
\(\Q(\zeta_{13})^+\) |
$6$ |
$[6, 0]$ |
79.1 |
\( 79 \) |
\( - 79^{2} \) |
$78.36687$ |
$(a^3-a^2-2a+3)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$45606.09482$ |
1.49691 |
\( \frac{628049103430807}{6241} a^{5} - \frac{182589231311538}{6241} a^{4} - \frac{3269795114557063}{6241} a^{3} + \frac{193031548929585}{6241} a^{2} + \frac{3905423405681707}{6241} a + \frac{885817850043621}{6241} \) |
\( \bigl[a^{4} - 3 a^{2} + a\) , \( -a^{4} + 3 a^{2} + a - 1\) , \( a^{4} - 3 a^{2} + a\) , \( 4 a^{5} - 10 a^{4} - 12 a^{3} + 30 a^{2} + 10 a - 21\) , \( -15 a^{5} + 27 a^{4} + 43 a^{3} - 71 a^{2} - 34 a + 43\bigr] \) |
${y}^2+\left(a^{4}-3a^{2}+a\right){x}{y}+\left(a^{4}-3a^{2}+a\right){y}={x}^{3}+\left(-a^{4}+3a^{2}+a-1\right){x}^{2}+\left(4a^{5}-10a^{4}-12a^{3}+30a^{2}+10a-21\right){x}-15a^{5}+27a^{4}+43a^{3}-71a^{2}-34a+43$ |
| 79.1-c4 |
79.1-c |
$4$ |
$10$ |
\(\Q(\zeta_{13})^+\) |
$6$ |
$[6, 0]$ |
79.1 |
\( 79 \) |
\( - 79^{10} \) |
$78.36687$ |
$(a^3-a^2-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$625$ |
\( 2 \) |
$1$ |
$2.918790068$ |
1.49691 |
\( \frac{127794683808852859853832701635933437922415}{9468276082626847201} a^{5} + \frac{120367721300657709905855839586570070913343}{9468276082626847201} a^{4} - \frac{405233310886078181372607580308878671807916}{9468276082626847201} a^{3} - \frac{275737199471198880155191606074376860275461}{9468276082626847201} a^{2} + \frac{231318547680046130469307232906240352482422}{9468276082626847201} a + \frac{65809650751079058294984275680386783414465}{9468276082626847201} \) |
\( \bigl[a^{4} - 3 a^{2} + a\) , \( -a^{4} + 3 a^{2} + a - 1\) , \( a^{4} - 3 a^{2} + a\) , \( 4 a^{5} - 200 a^{4} + 73 a^{3} + 365 a^{2} + 85 a - 231\) , \( 24 a^{5} - 2877 a^{4} + 1997 a^{3} + 4755 a^{2} - 931 a - 1732\bigr] \) |
${y}^2+\left(a^{4}-3a^{2}+a\right){x}{y}+\left(a^{4}-3a^{2}+a\right){y}={x}^{3}+\left(-a^{4}+3a^{2}+a-1\right){x}^{2}+\left(4a^{5}-200a^{4}+73a^{3}+365a^{2}+85a-231\right){x}+24a^{5}-2877a^{4}+1997a^{3}+4755a^{2}-931a-1732$ |
| 79.1-d1 |
79.1-d |
$8$ |
$12$ |
\(\Q(\zeta_{13})^+\) |
$6$ |
$[6, 0]$ |
79.1 |
\( 79 \) |
\( - 79^{3} \) |
$78.36687$ |
$(a^3-a^2-2a+3)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$16$ |
\( 1 \) |
$1$ |
$202.5393985$ |
1.32957 |
\( -\frac{2762735175183868847277552646275174}{493039} a^{5} - \frac{1373138770767122616960080619238639}{493039} a^{4} + \frac{11758057618620054164219573960351571}{493039} a^{3} + \frac{6551124309568948704114188838899166}{493039} a^{2} - \frac{6769237134468529246169518671845202}{493039} a - \frac{1845487978585672096436224846805198}{493039} \) |
\( \bigl[a^{5} - 5 a^{3} + 6 a\) , \( a^{5} + a^{4} - 4 a^{3} - 4 a^{2} + 2 a + 2\) , \( a^{2} + a - 1\) , \( -50 a^{5} - 47 a^{4} + 212 a^{3} + 148 a^{2} - 212 a - 107\) , \( -18 a^{5} + 417 a^{4} + 354 a^{3} - 1064 a^{2} - 530 a + 27\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+6a\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(a^{5}+a^{4}-4a^{3}-4a^{2}+2a+2\right){x}^{2}+\left(-50a^{5}-47a^{4}+212a^{3}+148a^{2}-212a-107\right){x}-18a^{5}+417a^{4}+354a^{3}-1064a^{2}-530a+27$ |
| 79.1-d2 |
79.1-d |
$8$ |
$12$ |
\(\Q(\zeta_{13})^+\) |
$6$ |
$[6, 0]$ |
79.1 |
\( 79 \) |
\( 79^{6} \) |
$78.36687$ |
$(a^3-a^2-2a+3)$ |
$0 \le r \le 2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$4$ |
\( 2 \) |
$1$ |
$1620.315188$ |
1.32957 |
\( -\frac{7947972766113080746071972}{243087455521} a^{5} - \frac{3950313317752480802186229}{243087455521} a^{4} + \frac{33826159878792106034273209}{243087455521} a^{3} + \frac{18846597413196990291447308}{243087455521} a^{2} - \frac{19474075142746010748953494}{243087455521} a - \frac{5309190805526992370823771}{243087455521} \) |
\( \bigl[a^{5} - 5 a^{3} + a^{2} + 6 a - 1\) , \( a^{5} + a^{4} - 4 a^{3} - 4 a^{2} + a + 2\) , \( a^{4} + a^{3} - 4 a^{2} - 3 a + 2\) , \( -45 a^{5} + 8 a^{4} + 237 a^{3} + 9 a^{2} - 282 a - 82\) , \( 78 a^{5} - 32 a^{4} - 397 a^{3} + 76 a^{2} + 458 a + 41\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+a^{2}+6a-1\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-3a+2\right){y}={x}^{3}+\left(a^{5}+a^{4}-4a^{3}-4a^{2}+a+2\right){x}^{2}+\left(-45a^{5}+8a^{4}+237a^{3}+9a^{2}-282a-82\right){x}+78a^{5}-32a^{4}-397a^{3}+76a^{2}+458a+41$ |
| 79.1-d3 |
79.1-d |
$8$ |
$12$ |
\(\Q(\zeta_{13})^+\) |
$6$ |
$[6, 0]$ |
79.1 |
\( 79 \) |
\( -79 \) |
$78.36687$ |
$(a^3-a^2-2a+3)$ |
$0 \le r \le 2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$12962.52150$ |
1.32957 |
\( \frac{229222312512}{79} a^{5} - \frac{489659661913}{79} a^{4} - \frac{589830121776}{79} a^{3} + \frac{1587030264768}{79} a^{2} - \frac{427631180184}{79} a - \frac{201808382600}{79} \) |
\( \bigl[a^{5} + a^{4} - 4 a^{3} - 3 a^{2} + 2 a\) , \( a^{5} - 5 a^{3} - a^{2} + 4 a + 2\) , \( a^{5} - 4 a^{3} + 2 a + 1\) , \( 10 a^{5} - 5 a^{4} - 46 a^{3} + 18 a^{2} + 40 a - 18\) , \( 12 a^{5} - 16 a^{4} - 57 a^{3} + 66 a^{2} + 60 a - 53\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-4a^{3}-3a^{2}+2a\right){x}{y}+\left(a^{5}-4a^{3}+2a+1\right){y}={x}^{3}+\left(a^{5}-5a^{3}-a^{2}+4a+2\right){x}^{2}+\left(10a^{5}-5a^{4}-46a^{3}+18a^{2}+40a-18\right){x}+12a^{5}-16a^{4}-57a^{3}+66a^{2}+60a-53$ |
| 79.1-d4 |
79.1-d |
$8$ |
$12$ |
\(\Q(\zeta_{13})^+\) |
$6$ |
$[6, 0]$ |
79.1 |
\( 79 \) |
\( - 79^{3} \) |
$78.36687$ |
$(a^3-a^2-2a+3)$ |
$0 \le r \le 2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$12962.52150$ |
1.32957 |
\( -\frac{1134795849368}{493039} a^{5} - \frac{640510493225}{493039} a^{4} + \frac{4738281412113}{493039} a^{3} + \frac{2951102426900}{493039} a^{2} - \frac{2417902662226}{493039} a - \frac{686687764294}{493039} \) |
\( \bigl[a^{5} - 4 a^{3} + 2 a + 1\) , \( a^{5} + a^{4} - 4 a^{3} - 4 a^{2} + 2 a + 1\) , \( a^{5} + a^{4} - 4 a^{3} - 4 a^{2} + 3 a + 3\) , \( 47 a^{5} + 24 a^{4} - 200 a^{3} - 114 a^{2} + 114 a + 32\) , \( 221 a^{5} + 109 a^{4} - 941 a^{3} - 521 a^{2} + 542 a + 145\bigr] \) |
${y}^2+\left(a^{5}-4a^{3}+2a+1\right){x}{y}+\left(a^{5}+a^{4}-4a^{3}-4a^{2}+3a+3\right){y}={x}^{3}+\left(a^{5}+a^{4}-4a^{3}-4a^{2}+2a+1\right){x}^{2}+\left(47a^{5}+24a^{4}-200a^{3}-114a^{2}+114a+32\right){x}+221a^{5}+109a^{4}-941a^{3}-521a^{2}+542a+145$ |
| 79.1-d5 |
79.1-d |
$8$ |
$12$ |
\(\Q(\zeta_{13})^+\) |
$6$ |
$[6, 0]$ |
79.1 |
\( 79 \) |
\( 79^{12} \) |
$78.36687$ |
$(a^3-a^2-2a+3)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$64$ |
\( 2 \) |
$1$ |
$25.31742482$ |
1.32957 |
\( \frac{2033369859844863642437231380090}{59091511031674153381441} a^{5} - \frac{4735260214072170447973367488703}{59091511031674153381441} a^{4} - \frac{3625278097962318215004518456861}{59091511031674153381441} a^{3} + \frac{14266749716321853993630284563838}{59091511031674153381441} a^{2} - \frac{8936329652263048501846210029746}{59091511031674153381441} a + \frac{1288287690387077768870911413346}{59091511031674153381441} \) |
\( \bigl[a^{5} - 5 a^{3} + a^{2} + 5 a - 2\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a^{3} - 3 a + 1\) , \( 97 a^{5} + 9 a^{4} - 446 a^{3} - 97 a^{2} + 388 a + 71\) , \( 349 a^{5} + 145 a^{4} - 1477 a^{3} - 737 a^{2} + 879 a + 185\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+a^{2}+5a-2\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-3\right){x}^{2}+\left(97a^{5}+9a^{4}-446a^{3}-97a^{2}+388a+71\right){x}+349a^{5}+145a^{4}-1477a^{3}-737a^{2}+879a+185$ |
| 79.1-d6 |
79.1-d |
$8$ |
$12$ |
\(\Q(\zeta_{13})^+\) |
$6$ |
$[6, 0]$ |
79.1 |
\( 79 \) |
\( 79^{2} \) |
$78.36687$ |
$(a^3-a^2-2a+3)$ |
$0 \le r \le 2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$4$ |
\( 2 \) |
$1$ |
$1620.315188$ |
1.32957 |
\( -\frac{51317863475416}{6241} a^{5} + \frac{1667446511596884}{6241} a^{4} + \frac{1365100078844124}{6241} a^{3} - \frac{5619927792030191}{6241} a^{2} - \frac{2413322991143088}{6241} a + \frac{3638886803263608}{6241} \) |
\( \bigl[a^{4} + a^{3} - 3 a^{2} - 2 a\) , \( a^{5} - a^{4} - 6 a^{3} + 5 a^{2} + 9 a - 3\) , \( a^{3} - 3 a\) , \( -14 a^{5} + 23 a^{4} + 53 a^{3} - 63 a^{2} - 16 a - 18\) , \( 9 a^{5} - 89 a^{4} + 90 a^{3} + 317 a^{2} - 346 a - 114\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-3a^{2}-2a\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{5}-a^{4}-6a^{3}+5a^{2}+9a-3\right){x}^{2}+\left(-14a^{5}+23a^{4}+53a^{3}-63a^{2}-16a-18\right){x}+9a^{5}-89a^{4}+90a^{3}+317a^{2}-346a-114$ |
| 79.1-d7 |
79.1-d |
$8$ |
$12$ |
\(\Q(\zeta_{13})^+\) |
$6$ |
$[6, 0]$ |
79.1 |
\( 79 \) |
\( -79 \) |
$78.36687$ |
$(a^3-a^2-2a+3)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$16$ |
\( 1 \) |
$1$ |
$202.5393985$ |
1.32957 |
\( \frac{14975057382763351033927532}{79} a^{5} + \frac{14104761450659533335839904}{79} a^{4} - \frac{47485481470815573950189484}{79} a^{3} - \frac{32311049678505073476173738}{79} a^{2} + \frac{27106045692032720097856969}{79} a + \frac{7711614205444837873329076}{79} \) |
\( \bigl[a^{4} + a^{3} - 3 a^{2} - 2 a\) , \( a^{5} - a^{4} - 6 a^{3} + 5 a^{2} + 9 a - 3\) , \( a^{3} - 3 a\) , \( -174 a^{5} + 48 a^{4} + 888 a^{3} - 53 a^{2} - 1036 a - 253\) , \( -1944 a^{5} + 404 a^{4} + 10398 a^{3} - 6 a^{2} - 12923 a - 2986\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-3a^{2}-2a\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{5}-a^{4}-6a^{3}+5a^{2}+9a-3\right){x}^{2}+\left(-174a^{5}+48a^{4}+888a^{3}-53a^{2}-1036a-253\right){x}-1944a^{5}+404a^{4}+10398a^{3}-6a^{2}-12923a-2986$ |
| 79.1-d8 |
79.1-d |
$8$ |
$12$ |
\(\Q(\zeta_{13})^+\) |
$6$ |
$[6, 0]$ |
79.1 |
\( 79 \) |
\( 79^{4} \) |
$78.36687$ |
$(a^3-a^2-2a+3)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$64$ |
\( 2 \) |
$1$ |
$25.31742482$ |
1.32957 |
\( -\frac{3050233510862210151986369219028}{38950081} a^{5} + \frac{3785563553688770366539690135200}{38950081} a^{4} + \frac{14338569026938982489863055482260}{38950081} a^{3} - \frac{15657581063688821579016146021962}{38950081} a^{2} - \frac{14526775380595228987077436189607}{38950081} a + \frac{12652719090941410050519681882308}{38950081} \) |
\( \bigl[a^{5} - 5 a^{3} + a^{2} + 6 a - 2\) , \( a^{5} + a^{4} - 6 a^{3} - 4 a^{2} + 7 a + 2\) , \( a^{5} + a^{4} - 4 a^{3} - 4 a^{2} + 2 a + 2\) , \( -269 a^{5} + 97 a^{4} + 1409 a^{3} - 146 a^{2} - 1715 a - 393\) , \( 70265 a^{5} + 38655 a^{4} - 294531 a^{3} - 179297 a^{2} + 154272 a + 43383\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+a^{2}+6a-2\right){x}{y}+\left(a^{5}+a^{4}-4a^{3}-4a^{2}+2a+2\right){y}={x}^{3}+\left(a^{5}+a^{4}-6a^{3}-4a^{2}+7a+2\right){x}^{2}+\left(-269a^{5}+97a^{4}+1409a^{3}-146a^{2}-1715a-393\right){x}+70265a^{5}+38655a^{4}-294531a^{3}-179297a^{2}+154272a+43383$ |
*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.
