| 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 |
| 79.2-a1 |
79.2-a |
$2$ |
$2$ |
\(\Q(\zeta_{13})^+\) |
$6$ |
$[6, 0]$ |
79.2 |
\( 79 \) |
\( -79 \) |
$78.36687$ |
$(a^5-4a^3-a^2+2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.019263609$ |
$53060.19998$ |
2.51617 |
\( -\frac{19238641932}{79} a^{5} + \frac{23876631104}{79} a^{4} + \frac{90437151053}{79} a^{3} - \frac{98756765310}{79} a^{2} - \frac{91624179396}{79} a + \frac{79804268844}{79} \) |
\( \bigl[a^{5} - 4 a^{3} + a^{2} + 2 a - 2\) , \( a^{4} - 5 a^{2} + 4\) , \( a^{4} - 4 a^{2} + 2\) , \( -a^{5} + 3 a^{4} + 4 a^{3} - 12 a^{2} - 3 a + 8\) , \( 5 a^{5} - 10 a^{4} - 13 a^{3} + 32 a^{2} - 9 a - 3\bigr] \) |
${y}^2+\left(a^{5}-4a^{3}+a^{2}+2a-2\right){x}{y}+\left(a^{4}-4a^{2}+2\right){y}={x}^{3}+\left(a^{4}-5a^{2}+4\right){x}^{2}+\left(-a^{5}+3a^{4}+4a^{3}-12a^{2}-3a+8\right){x}+5a^{5}-10a^{4}-13a^{3}+32a^{2}-9a-3$ |
| 79.2-a2 |
79.2-a |
$2$ |
$2$ |
\(\Q(\zeta_{13})^+\) |
$6$ |
$[6, 0]$ |
79.2 |
\( 79 \) |
\( - 79^{2} \) |
$78.36687$ |
$(a^5-4a^3-a^2+2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.038527218$ |
$13265.04999$ |
2.51617 |
\( -\frac{1827330655296306713158}{6241} a^{5} + \frac{2267851397132794939683}{6241} a^{4} + \frac{8589934719036282821459}{6241} a^{3} - \frac{9380127050470680153907}{6241} a^{2} - \frac{8702685181704913513870}{6241} a + \frac{7579977528109156697231}{6241} \) |
\( \bigl[a^{5} - 4 a^{3} + a^{2} + 2 a - 2\) , \( a^{4} - 5 a^{2} + 4\) , \( a^{4} - 4 a^{2} + 2\) , \( -16 a^{5} + 43 a^{4} + 24 a^{3} - 132 a^{2} + 82 a - 7\) , \( 127 a^{5} - 279 a^{4} - 308 a^{3} + 894 a^{2} - 296 a - 82\bigr] \) |
${y}^2+\left(a^{5}-4a^{3}+a^{2}+2a-2\right){x}{y}+\left(a^{4}-4a^{2}+2\right){y}={x}^{3}+\left(a^{4}-5a^{2}+4\right){x}^{2}+\left(-16a^{5}+43a^{4}+24a^{3}-132a^{2}+82a-7\right){x}+127a^{5}-279a^{4}-308a^{3}+894a^{2}-296a-82$ |
| 79.2-b1 |
79.2-b |
$1$ |
$1$ |
\(\Q(\zeta_{13})^+\) |
$6$ |
$[6, 0]$ |
79.2 |
\( 79 \) |
\( 79^{2} \) |
$78.36687$ |
$(a^5-4a^3-a^2+2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.001171369$ |
$107610.2235$ |
2.48239 |
\( \frac{58199203663}{6241} a^{5} + \frac{29929897535}{6241} a^{4} - \frac{246476187924}{6241} a^{3} - \frac{141422125490}{6241} a^{2} + \frac{137785461801}{6241} a + \frac{37929353079}{6241} \) |
\( \bigl[a^{5} + a^{4} - 5 a^{3} - 3 a^{2} + 6 a\) , \( a^{4} - 3 a^{2} + a - 1\) , \( a^{4} + a^{3} - 4 a^{2} - 2 a + 3\) , \( 9 a^{5} + 7 a^{4} - 35 a^{3} - 27 a^{2} + 16 a + 8\) , \( -16 a^{5} - 8 a^{4} + 71 a^{3} + 45 a^{2} - 37 a - 13\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-5a^{3}-3a^{2}+6a\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-2a+3\right){y}={x}^{3}+\left(a^{4}-3a^{2}+a-1\right){x}^{2}+\left(9a^{5}+7a^{4}-35a^{3}-27a^{2}+16a+8\right){x}-16a^{5}-8a^{4}+71a^{3}+45a^{2}-37a-13$ |
| 79.2-c1 |
79.2-c |
$4$ |
$10$ |
\(\Q(\zeta_{13})^+\) |
$6$ |
$[6, 0]$ |
79.2 |
\( 79 \) |
\( -79 \) |
$78.36687$ |
$(a^5-4a^3-a^2+2a+3)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$91212.18964$ |
1.49691 |
\( \frac{3687355}{79} a^{5} + \frac{3709875}{79} a^{4} - \frac{11701462}{79} a^{3} - \frac{8651526}{79} a^{2} + \frac{6794485}{79} a + \frac{2106798}{79} \) |
\( \bigl[a^{4} - 3 a^{2} + a + 1\) , \( a^{4} + a^{3} - 5 a^{2} - 2 a + 4\) , \( a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 5 a + 2\) , \( a^{5} + 5 a^{4} - 2 a^{3} - 14 a^{2} + 6\) , \( 3 a^{5} + 4 a^{4} - 8 a^{3} - 10 a^{2} + 3 a + 3\bigr] \) |
${y}^2+\left(a^{4}-3a^{2}+a+1\right){x}{y}+\left(a^{5}+a^{4}-5a^{3}-4a^{2}+5a+2\right){y}={x}^{3}+\left(a^{4}+a^{3}-5a^{2}-2a+4\right){x}^{2}+\left(a^{5}+5a^{4}-2a^{3}-14a^{2}+6\right){x}+3a^{5}+4a^{4}-8a^{3}-10a^{2}+3a+3$ |
| 79.2-c2 |
79.2-c |
$4$ |
$10$ |
\(\Q(\zeta_{13})^+\) |
$6$ |
$[6, 0]$ |
79.2 |
\( 79 \) |
\( - 79^{2} \) |
$78.36687$ |
$(a^5-4a^3-a^2+2a+3)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$45606.09482$ |
1.49691 |
\( \frac{193939865007050}{6241} a^{5} + \frac{182589231311538}{6241} a^{4} - \frac{614963180030221}{6241} a^{3} - \frac{418218096531586}{6241} a^{2} + \frac{350950762139432}{6241} a + \frac{99835596539045}{6241} \) |
\( \bigl[a^{4} - 3 a^{2} + a + 1\) , \( a^{4} + a^{3} - 5 a^{2} - 2 a + 4\) , \( a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 5 a + 2\) , \( 6 a^{5} + 15 a^{4} - 27 a^{3} - 54 a^{2} + 20 a + 16\) , \( -24 a^{5} - 17 a^{4} + 112 a^{3} + 78 a^{2} - 80 a - 16\bigr] \) |
${y}^2+\left(a^{4}-3a^{2}+a+1\right){x}{y}+\left(a^{5}+a^{4}-5a^{3}-4a^{2}+5a+2\right){y}={x}^{3}+\left(a^{4}+a^{3}-5a^{2}-2a+4\right){x}^{2}+\left(6a^{5}+15a^{4}-27a^{3}-54a^{2}+20a+16\right){x}-24a^{5}-17a^{4}+112a^{3}+78a^{2}-80a-16$ |
| 79.2-c3 |
79.2-c |
$4$ |
$10$ |
\(\Q(\zeta_{13})^+\) |
$6$ |
$[6, 0]$ |
79.2 |
\( 79 \) |
\( - 79^{5} \) |
$78.36687$ |
$(a^5-4a^3-a^2+2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$625$ |
\( 1 \) |
$1$ |
$5.837580137$ |
1.49691 |
\( -\frac{95687653313364719174851}{3077056399} a^{5} + \frac{118530438657502667153870}{3077056399} a^{4} + \frac{449749253784052398980356}{3077056399} a^{3} - \frac{489631089072919358186908}{3077056399} a^{2} - \frac{455878360751499749698808}{3077056399} a + \frac{395013443228849567484072}{3077056399} \) |
\( \bigl[a^{4} - 3 a^{2} + a + 1\) , \( a^{4} + a^{3} - 5 a^{2} - 2 a + 4\) , \( a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 5 a + 2\) , \( 66 a^{5} - 60 a^{4} - 292 a^{3} + 256 a^{2} + 250 a - 254\) , \( 536 a^{5} - 544 a^{4} - 2472 a^{3} + 2270 a^{2} + 2330 a - 2043\bigr] \) |
${y}^2+\left(a^{4}-3a^{2}+a+1\right){x}{y}+\left(a^{5}+a^{4}-5a^{3}-4a^{2}+5a+2\right){y}={x}^{3}+\left(a^{4}+a^{3}-5a^{2}-2a+4\right){x}^{2}+\left(66a^{5}-60a^{4}-292a^{3}+256a^{2}+250a-254\right){x}+536a^{5}-544a^{4}-2472a^{3}+2270a^{2}+2330a-2043$ |
| 79.2-c4 |
79.2-c |
$4$ |
$10$ |
\(\Q(\zeta_{13})^+\) |
$6$ |
$[6, 0]$ |
79.2 |
\( 79 \) |
\( - 79^{10} \) |
$78.36687$ |
$(a^5-4a^3-a^2+2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$625$ |
\( 2 \) |
$1$ |
$2.918790068$ |
1.49691 |
\( \frac{413933174410997894795667347925508787196167}{9468276082626847201} a^{5} - \frac{120367721300657709905855839586570070913343}{9468276082626847201} a^{4} - \frac{2155031836485763723540712652312877288445403}{9468276082626847201} a^{3} + \frac{127363055743787011821011590888921694935870}{9468276082626847201} a^{2} + \frac{2573926170456822792425153018906047502210297}{9468276082626847201} a + \frac{583654074628342083306992117206060453038576}{9468276082626847201} \) |
\( \bigl[a^{5} - 5 a^{3} + a^{2} + 6 a - 1\) , \( a^{5} + a^{4} - 6 a^{3} - 5 a^{2} + 7 a + 4\) , \( a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 5 a + 3\) , \( -374 a^{5} - 33 a^{4} + 1737 a^{3} + 125 a^{2} - 1818 a - 430\) , \( -5000 a^{5} - 11 a^{4} + 24043 a^{3} + 1223 a^{2} - 26468 a - 6156\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+a^{2}+6a-1\right){x}{y}+\left(a^{5}+a^{4}-5a^{3}-4a^{2}+5a+3\right){y}={x}^{3}+\left(a^{5}+a^{4}-6a^{3}-5a^{2}+7a+4\right){x}^{2}+\left(-374a^{5}-33a^{4}+1737a^{3}+125a^{2}-1818a-430\right){x}-5000a^{5}-11a^{4}+24043a^{3}+1223a^{2}-26468a-6156$ |
| 79.2-d1 |
79.2-d |
$8$ |
$12$ |
\(\Q(\zeta_{13})^+\) |
$6$ |
$[6, 0]$ |
79.2 |
\( 79 \) |
\( 79^{4} \) |
$78.36687$ |
$(a^5-4a^3-a^2+2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$64$ |
\( 2 \) |
$1$ |
$25.31742482$ |
1.32957 |
\( \frac{1772160145288387329187728202093}{38950081} a^{5} - \frac{3785563553688770366539690135200}{38950081} a^{4} - \frac{4559910323819426166541565394103}{38950081} a^{3} + \frac{12269289188438379369687861018480}{38950081} a^{2} - \frac{3306540438599034577699264922449}{38950081} a - \frac{1559822322736517814951740711376}{38950081} \) |
\( \bigl[a^{5} - 4 a^{3} + 2 a + 1\) , \( a^{5} + a^{4} - 4 a^{3} - 4 a^{2} + 2 a + 1\) , \( a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 6 a + 2\) , \( 147 a^{5} - 135 a^{4} - 685 a^{3} + 554 a^{2} + 657 a - 495\) , \( 513 a^{5} - 795 a^{4} - 1459 a^{3} + 1794 a^{2} + 1061 a - 1027\bigr] \) |
${y}^2+\left(a^{5}-4a^{3}+2a+1\right){x}{y}+\left(a^{5}+a^{4}-5a^{3}-4a^{2}+6a+2\right){y}={x}^{3}+\left(a^{5}+a^{4}-4a^{3}-4a^{2}+2a+1\right){x}^{2}+\left(147a^{5}-135a^{4}-685a^{3}+554a^{2}+657a-495\right){x}+513a^{5}-795a^{4}-1459a^{3}+1794a^{2}+1061a-1027$ |
| 79.2-d2 |
79.2-d |
$8$ |
$12$ |
\(\Q(\zeta_{13})^+\) |
$6$ |
$[6, 0]$ |
79.2 |
\( 79 \) |
\( - 79^{3} \) |
$78.36687$ |
$(a^5-4a^3-a^2+2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$12962.52150$ |
1.32957 |
\( -\frac{191527412792}{493039} a^{5} + \frac{640510493225}{493039} a^{4} - \frac{71933883265}{493039} a^{3} - \frac{985833644948}{493039} a^{2} + \frac{355769435122}{493039} a + \frac{141568953927}{493039} \) |
\( \bigl[a^{5} - 5 a^{3} + a^{2} + 6 a - 2\) , \( a^{5} + a^{4} - 6 a^{3} - 4 a^{2} + 7 a + 2\) , \( a^{4} + a^{3} - 3 a^{2} - 3 a\) , \( a^{5} - 2 a^{4} - 8 a^{3} + 4 a^{2} + 16 a + 7\) , \( 18 a^{5} - 5 a^{4} - 92 a^{3} + 3 a^{2} + 107 a + 25\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+a^{2}+6a-2\right){x}{y}+\left(a^{4}+a^{3}-3a^{2}-3a\right){y}={x}^{3}+\left(a^{5}+a^{4}-6a^{3}-4a^{2}+7a+2\right){x}^{2}+\left(a^{5}-2a^{4}-8a^{3}+4a^{2}+16a+7\right){x}+18a^{5}-5a^{4}-92a^{3}+3a^{2}+107a+25$ |
| 79.2-d3 |
79.2-d |
$8$ |
$12$ |
\(\Q(\zeta_{13})^+\) |
$6$ |
$[6, 0]$ |
79.2 |
\( 79 \) |
\( 79^{12} \) |
$78.36687$ |
$(a^5-4a^3-a^2+2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$64$ |
\( 2 \) |
$1$ |
$25.31742482$ |
1.32957 |
\( -\frac{4213725561773537170460819088132}{59091511031674153381441} a^{5} + \frac{4735260214072170447973367488703}{59091511031674153381441} a^{4} + \frac{21007658734762343202593913342931}{59091511031674153381441} a^{3} - \frac{20747351843478511341101740909698}{59091511031674153381441} a^{2} - \frac{23587610940778964708709685256086}{59091511031674153381441} a + \frac{19228628455193933510627919984685}{59091511031674153381441} \) |
\( \bigl[a^{3} - 2 a\) , \( -a^{4} - a^{3} + 5 a^{2} + 3 a - 5\) , \( a^{5} - 4 a^{3} + a^{2} + 2 a - 1\) , \( 25 a^{5} - 7 a^{4} - 59 a^{3} - 20 a^{2} + 28 a + 6\) , \( 115 a^{5} - 157 a^{4} - 177 a^{3} + 163 a^{2} + 12 a - 9\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a^{5}-4a^{3}+a^{2}+2a-1\right){y}={x}^{3}+\left(-a^{4}-a^{3}+5a^{2}+3a-5\right){x}^{2}+\left(25a^{5}-7a^{4}-59a^{3}-20a^{2}+28a+6\right){x}+115a^{5}-157a^{4}-177a^{3}+163a^{2}+12a-9$ |
| 79.2-d4 |
79.2-d |
$8$ |
$12$ |
\(\Q(\zeta_{13})^+\) |
$6$ |
$[6, 0]$ |
79.2 |
\( 79 \) |
\( -79 \) |
$78.36687$ |
$(a^5-4a^3-a^2+2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$12962.52150$ |
1.32957 |
\( -\frac{394558082305}{79} a^{5} + \frac{489659661913}{79} a^{4} + \frac{1854739132496}{79} a^{3} - \frac{2025260426523}{79} a^{2} - \frac{1879073923839}{79} a + \frac{1636516718939}{79} \) |
\( \bigl[a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 6 a + 2\) , \( a^{5} - 6 a^{3} - a^{2} + 8 a + 1\) , \( a^{2} - 2\) , \( -a^{5} + 3 a^{4} + 7 a^{3} - 10 a^{2} - 15 a - 3\) , \( 10 a^{5} + 3 a^{4} - 45 a^{3} - 17 a^{2} + 34 a + 8\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-5a^{3}-4a^{2}+6a+2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{5}-6a^{3}-a^{2}+8a+1\right){x}^{2}+\left(-a^{5}+3a^{4}+7a^{3}-10a^{2}-15a-3\right){x}+10a^{5}+3a^{4}-45a^{3}-17a^{2}+34a+8$ |
| 79.2-d5 |
79.2-d |
$8$ |
$12$ |
\(\Q(\zeta_{13})^+\) |
$6$ |
$[6, 0]$ |
79.2 |
\( 79 \) |
\( 79^{2} \) |
$78.36687$ |
$(a^5-4a^3-a^2+2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$4$ |
\( 2 \) |
$1$ |
$1620.315188$ |
1.32957 |
\( \frac{2836245122232008}{6241} a^{5} - \frac{1667446511596884}{6241} a^{4} - \frac{13563637353920501}{6241} a^{3} + \frac{3893828773323608}{6241} a^{2} + \frac{13944589487562891}{6241} a + \frac{2953285300121734}{6241} \) |
\( \bigl[a^{4} - 4 a^{2} + a + 3\) , \( -a^{5} + 5 a^{3} - 4 a - 1\) , \( a^{5} - 4 a^{3} + 3 a + 1\) , \( 13 a^{5} - 19 a^{4} - 71 a^{3} + 80 a^{2} + 83 a - 81\) , \( -72 a^{5} + 78 a^{4} + 309 a^{3} - 342 a^{2} - 282 a + 267\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a+3\right){x}{y}+\left(a^{5}-4a^{3}+3a+1\right){y}={x}^{3}+\left(-a^{5}+5a^{3}-4a-1\right){x}^{2}+\left(13a^{5}-19a^{4}-71a^{3}+80a^{2}+83a-81\right){x}-72a^{5}+78a^{4}+309a^{3}-342a^{2}-282a+267$ |
| 79.2-d6 |
79.2-d |
$8$ |
$12$ |
\(\Q(\zeta_{13})^+\) |
$6$ |
$[6, 0]$ |
79.2 |
\( 79 \) |
\( 79^{6} \) |
$78.36687$ |
$(a^5-4a^3-a^2+2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$4$ |
\( 2 \) |
$1$ |
$1620.315188$ |
1.32957 |
\( -\frac{1425636485252980909039816}{243087455521} a^{5} + \frac{3950313317752480802186229}{243087455521} a^{4} + \frac{132524966325356660310459}{243087455521} a^{3} - \frac{5937236001484144710472036}{243087455521} a^{2} + \frac{1960503869688177561208582}{243087455521} a + \frac{805029528557988808966398}{243087455521} \) |
\( \bigl[a^{4} + a^{3} - 3 a^{2} - 3 a\) , \( -a^{5} - a^{4} + 5 a^{3} + 3 a^{2} - 6 a\) , \( a^{5} - 4 a^{3} + a^{2} + 3 a - 2\) , \( -122 a^{5} + 279 a^{4} + 299 a^{3} - 910 a^{2} + 266 a + 113\) , \( -1672 a^{5} + 3560 a^{4} + 4304 a^{3} - 11532 a^{2} + 3118 a + 1453\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-3a^{2}-3a\right){x}{y}+\left(a^{5}-4a^{3}+a^{2}+3a-2\right){y}={x}^{3}+\left(-a^{5}-a^{4}+5a^{3}+3a^{2}-6a\right){x}^{2}+\left(-122a^{5}+279a^{4}+299a^{3}-910a^{2}+266a+113\right){x}-1672a^{5}+3560a^{4}+4304a^{3}-11532a^{2}+3118a+1453$ |
| 79.2-d7 |
79.2-d |
$8$ |
$12$ |
\(\Q(\zeta_{13})^+\) |
$6$ |
$[6, 0]$ |
79.2 |
\( 79 \) |
\( -79 \) |
$78.36687$ |
$(a^5-4a^3-a^2+2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$16$ |
\( 1 \) |
$1$ |
$202.5393985$ |
1.32957 |
\( \frac{48504936557879041922403741}{79} a^{5} - \frac{14104761450659533335839904}{79} a^{4} - \frac{252527917462868736143364679}{79} a^{3} + \frac{14924478908977418788071536}{79} a^{2} + \frac{301614205643238673575824063}{79} a + \frac{68392932987734720039077472}{79} \) |
\( \bigl[a^{4} - 4 a^{2} + a + 3\) , \( -a^{5} + 5 a^{3} - 4 a - 1\) , \( a^{5} - 4 a^{3} + 3 a + 1\) , \( -77 a^{5} - 44 a^{4} + 294 a^{3} + 120 a^{2} - 247 a - 101\) , \( -622 a^{5} - 430 a^{4} + 1883 a^{3} + 559 a^{2} - 874 a + 545\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a+3\right){x}{y}+\left(a^{5}-4a^{3}+3a+1\right){y}={x}^{3}+\left(-a^{5}+5a^{3}-4a-1\right){x}^{2}+\left(-77a^{5}-44a^{4}+294a^{3}+120a^{2}-247a-101\right){x}-622a^{5}-430a^{4}+1883a^{3}+559a^{2}-874a+545$ |
| 79.2-d8 |
79.2-d |
$8$ |
$12$ |
\(\Q(\zeta_{13})^+\) |
$6$ |
$[6, 0]$ |
79.2 |
\( 79 \) |
\( - 79^{3} \) |
$78.36687$ |
$(a^5-4a^3-a^2+2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$16$ |
\( 1 \) |
$1$ |
$202.5393985$ |
1.32957 |
\( -\frac{495554801214177843246403872780868}{493039} a^{5} + \frac{1373138770767122616960080619238639}{493039} a^{4} + \frac{46066008803308362998072382721091}{493039} a^{3} - \frac{2063798055002077778712052586691618}{493039} a^{2} + \frac{681476039780861879232188314131594}{493039} a + \frac{279830272118032082655371192751341}{493039} \) |
\( \bigl[a^{3} - 3 a + 1\) , \( -a^{5} + a^{4} + 4 a^{3} - 5 a^{2} - 3 a + 5\) , \( a^{5} + a^{4} - 4 a^{3} - 3 a^{2} + 3 a\) , \( -146 a^{5} + 270 a^{4} + 426 a^{3} - 917 a^{2} + 127 a + 175\) , \( 1626 a^{5} - 3224 a^{4} - 4926 a^{3} + 10781 a^{2} - 670 a - 2666\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{5}+a^{4}-4a^{3}-3a^{2}+3a\right){y}={x}^{3}+\left(-a^{5}+a^{4}+4a^{3}-5a^{2}-3a+5\right){x}^{2}+\left(-146a^{5}+270a^{4}+426a^{3}-917a^{2}+127a+175\right){x}+1626a^{5}-3224a^{4}-4926a^{3}+10781a^{2}-670a-2666$ |
*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.
