| 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 |
| 31.1-a1 |
31.1-a |
$12$ |
$24$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( - 31^{3} \) |
$82.86011$ |
$(2a^5-3a^4-8a^3+10a^2+5a-4)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$16$ |
\( 1 \) |
$1$ |
$1025.792884$ |
1.47276 |
\( \frac{1147749328284888733960618795900}{29791} a^{5} + \frac{141486795916680191166008423527}{29791} a^{4} - \frac{4290582183397657085249138615742}{29791} a^{3} + \frac{71916226788811881170252052327}{29791} a^{2} + \frac{2448196457529426302571246462997}{29791} a - \frac{540556579537374458371365865485}{29791} \) |
\( \bigl[2 a^{5} - 2 a^{4} - 9 a^{3} + 7 a^{2} + 7 a - 2\) , \( -2 a^{5} + 3 a^{4} + 8 a^{3} - 9 a^{2} - 4 a + 3\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 6 a^{2} - 2 a + 1\) , \( -11 a^{5} - 5 a^{4} + 48 a^{3} + 67 a^{2} - 90 a - 63\) , \( -337 a^{5} + 1380 a^{4} - 1160 a^{3} - 1156 a^{2} + 1361 a - 13\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-9a^{3}+7a^{2}+7a-2\right){x}{y}+\left(-a^{5}+2a^{4}+4a^{3}-6a^{2}-2a+1\right){y}={x}^{3}+\left(-2a^{5}+3a^{4}+8a^{3}-9a^{2}-4a+3\right){x}^{2}+\left(-11a^{5}-5a^{4}+48a^{3}+67a^{2}-90a-63\right){x}-337a^{5}+1380a^{4}-1160a^{3}-1156a^{2}+1361a-13$ |
| 31.1-a2 |
31.1-a |
$12$ |
$24$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( 31^{8} \) |
$82.86011$ |
$(2a^5-3a^4-8a^3+10a^2+5a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1024$ |
\( 2 \) |
$1$ |
$2.003501727$ |
1.47276 |
\( -\frac{1033073743235841200494976959934}{852891037441} a^{5} + \frac{3933929786659871173277923782815}{852891037441} a^{4} - \frac{2975097977593569902108674723259}{852891037441} a^{3} - \frac{2901568778559675791252921941164}{852891037441} a^{2} + \frac{3183623527721495073846445577852}{852891037441} a - \frac{573680380524522897838041437515}{852891037441} \) |
\( \bigl[a^{3} - 2 a\) , \( -a^{4} + a^{3} + 4 a^{2} - a - 3\) , \( 2 a^{5} - 2 a^{4} - 9 a^{3} + 7 a^{2} + 7 a - 2\) , \( 36 a^{5} + 139 a^{4} - 258 a^{3} - 563 a^{2} + 330 a - 79\) , \( 1873 a^{5} + 784 a^{4} - 9619 a^{3} - 4432 a^{2} + 7810 a - 1392\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}+\left(2a^{5}-2a^{4}-9a^{3}+7a^{2}+7a-2\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-a-3\right){x}^{2}+\left(36a^{5}+139a^{4}-258a^{3}-563a^{2}+330a-79\right){x}+1873a^{5}+784a^{4}-9619a^{3}-4432a^{2}+7810a-1392$ |
| 31.1-a3 |
31.1-a |
$12$ |
$24$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( 31^{6} \) |
$82.86011$ |
$(2a^5-3a^4-8a^3+10a^2+5a-4)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$4$ |
\( 2 \) |
$1$ |
$8206.343077$ |
1.47276 |
\( \frac{1460546550652965787030}{887503681} a^{5} + \frac{180239481432461299101}{887503681} a^{4} - \frac{5459549052609937959965}{887503681} a^{3} + \frac{91383042197658996772}{887503681} a^{2} + \frac{3115193703304519977774}{887503681} a - \frac{687821042793429817941}{887503681} \) |
\( \bigl[2 a^{5} - 2 a^{4} - 9 a^{3} + 7 a^{2} + 7 a - 2\) , \( -2 a^{5} + 3 a^{4} + 8 a^{3} - 9 a^{2} - 4 a + 3\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 6 a^{2} - 2 a + 1\) , \( 9 a^{5} - 40 a^{4} + 38 a^{3} + 32 a^{2} - 35 a + 2\) , \( -85 a^{5} + 329 a^{4} - 255 a^{3} - 243 a^{2} + 270 a - 47\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-9a^{3}+7a^{2}+7a-2\right){x}{y}+\left(-a^{5}+2a^{4}+4a^{3}-6a^{2}-2a+1\right){y}={x}^{3}+\left(-2a^{5}+3a^{4}+8a^{3}-9a^{2}-4a+3\right){x}^{2}+\left(9a^{5}-40a^{4}+38a^{3}+32a^{2}-35a+2\right){x}-85a^{5}+329a^{4}-255a^{3}-243a^{2}+270a-47$ |
| 31.1-a4 |
31.1-a |
$12$ |
$24$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( 31^{24} \) |
$82.86011$ |
$(2a^5-3a^4-8a^3+10a^2+5a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1024$ |
\( 2 \) |
$1$ |
$2.003501727$ |
1.47276 |
\( \frac{308629524306573180705764124400765214989728416}{620412660965527688188300451573157121} a^{5} - \frac{96678377635333373686040740401662681795239150}{620412660965527688188300451573157121} a^{4} - \frac{1398478163616726416481971891411691120456947555}{620412660965527688188300451573157121} a^{3} + \frac{111294770463329935355252104822968002094080011}{620412660965527688188300451573157121} a^{2} + \frac{807036468907095340993839638491373208865016181}{620412660965527688188300451573157121} a - \frac{182510843354625433266392408147536567243503960}{620412660965527688188300451573157121} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 5 a - 1\) , \( a^{5} - 6 a^{3} + 7 a + 2\) , \( a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 2 a\) , \( -2340 a^{5} + 3083 a^{4} + 11588 a^{3} - 10918 a^{2} - 12508 a + 3176\) , \( -82115 a^{5} + 108051 a^{4} + 403418 a^{3} - 382074 a^{2} - 428431 a + 118082\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+5a-1\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+3a^{2}+2a\right){y}={x}^{3}+\left(a^{5}-6a^{3}+7a+2\right){x}^{2}+\left(-2340a^{5}+3083a^{4}+11588a^{3}-10918a^{2}-12508a+3176\right){x}-82115a^{5}+108051a^{4}+403418a^{3}-382074a^{2}-428431a+118082$ |
| 31.1-a5 |
31.1-a |
$12$ |
$24$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( -31 \) |
$82.86011$ |
$(2a^5-3a^4-8a^3+10a^2+5a-4)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$65650.74461$ |
1.47276 |
\( \frac{349745746}{31} a^{5} - \frac{614724517}{31} a^{4} - \frac{1548446203}{31} a^{3} + \frac{2422385572}{31} a^{2} + \frac{1289061786}{31} a - \frac{1434751947}{31} \) |
\( \bigl[-2 a^{5} + 3 a^{4} + 9 a^{3} - 10 a^{2} - 8 a + 3\) , \( -a^{5} + 5 a^{3} + a^{2} - 5 a - 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+\left(-2a^{5}+3a^{4}+9a^{3}-10a^{2}-8a+3\right){x}{y}={x}^{3}+\left(-a^{5}+5a^{3}+a^{2}-5a-1\right){x}^{2}+{x}$ |
| 31.1-a6 |
31.1-a |
$12$ |
$24$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( - 31^{3} \) |
$82.86011$ |
$(2a^5-3a^4-8a^3+10a^2+5a-4)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$65650.74461$ |
1.47276 |
\( -\frac{488148481814}{29791} a^{5} + \frac{1817229407860}{29791} a^{4} - \frac{1334351754367}{29791} a^{3} - \frac{1342176233637}{29791} a^{2} + \frac{1446135272219}{29791} a - \frac{259491223572}{29791} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 5 a - 1\) , \( a^{5} - 6 a^{3} + 7 a + 2\) , \( a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 2 a\) , \( -5 a^{5} + 8 a^{4} + 23 a^{3} - 28 a^{2} - 23 a + 11\) , \( 28 a^{5} - 36 a^{4} - 138 a^{3} + 127 a^{2} + 147 a - 39\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+5a-1\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+3a^{2}+2a\right){y}={x}^{3}+\left(a^{5}-6a^{3}+7a+2\right){x}^{2}+\left(-5a^{5}+8a^{4}+23a^{3}-28a^{2}-23a+11\right){x}+28a^{5}-36a^{4}-138a^{3}+127a^{2}+147a-39$ |
| 31.1-a7 |
31.1-a |
$12$ |
$24$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( 31^{2} \) |
$82.86011$ |
$(2a^5-3a^4-8a^3+10a^2+5a-4)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$4$ |
\( 2 \) |
$1$ |
$8206.343077$ |
1.47276 |
\( -\frac{350193349920473908}{961} a^{5} + \frac{614989688312525919}{961} a^{4} + \frac{1550742937477348718}{961} a^{3} - \frac{2423388078335799313}{961} a^{2} - \frac{1291346530388574699}{961} a + \frac{1436064511168210027}{961} \) |
\( \bigl[-2 a^{5} + 3 a^{4} + 9 a^{3} - 10 a^{2} - 8 a + 3\) , \( -a^{5} + 5 a^{3} + a^{2} - 5 a - 1\) , \( 0\) , \( -4\) , \( -2 a^{5} + 8 a^{4} + 9 a^{3} - 33 a^{2} - 9 a + 12\bigr] \) |
${y}^2+\left(-2a^{5}+3a^{4}+9a^{3}-10a^{2}-8a+3\right){x}{y}={x}^{3}+\left(-a^{5}+5a^{3}+a^{2}-5a-1\right){x}^{2}-4{x}-2a^{5}+8a^{4}+9a^{3}-33a^{2}-9a+12$ |
| 31.1-a8 |
31.1-a |
$12$ |
$24$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( 31^{4} \) |
$82.86011$ |
$(2a^5-3a^4-8a^3+10a^2+5a-4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$64$ |
\( 2 \) |
$1$ |
$128.2241105$ |
1.47276 |
\( \frac{161977561667364262506242}{923521} a^{5} - \frac{474485436612723225705736}{923521} a^{4} - \frac{206957557465744779382665}{923521} a^{3} + \frac{1488151984849774698530977}{923521} a^{2} - \frac{1059026459496257469864311}{923521} a + \frac{174295328969264546943196}{923521} \) |
\( \bigl[-2 a^{5} + 3 a^{4} + 9 a^{3} - 10 a^{2} - 8 a + 3\) , \( -a^{5} + 5 a^{3} + a^{2} - 5 a - 1\) , \( 0\) , \( -10 a^{5} + 40 a^{4} + 45 a^{3} - 165 a^{2} - 45 a + 16\) , \( 6 a^{5} + 153 a^{4} - 31 a^{3} - 678 a^{2} - 36 a + 57\bigr] \) |
${y}^2+\left(-2a^{5}+3a^{4}+9a^{3}-10a^{2}-8a+3\right){x}{y}={x}^{3}+\left(-a^{5}+5a^{3}+a^{2}-5a-1\right){x}^{2}+\left(-10a^{5}+40a^{4}+45a^{3}-165a^{2}-45a+16\right){x}+6a^{5}+153a^{4}-31a^{3}-678a^{2}-36a+57$ |
| 31.1-a9 |
31.1-a |
$12$ |
$24$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( 31^{12} \) |
$82.86011$ |
$(2a^5-3a^4-8a^3+10a^2+5a-4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$64$ |
\( 2 \) |
$1$ |
$128.2241105$ |
1.47276 |
\( -\frac{1127683403680349712780740748443904004}{787662783788549761} a^{5} + \frac{354688222610355323886840898021118087}{787662783788549761} a^{4} + \frac{5108550614403361265287641142493913090}{787662783788549761} a^{3} - \frac{411149191401225017208777070394047609}{787662783788549761} a^{2} - \frac{2948347178168149967480663778467655563}{787662783788549761} a + \frac{669060970718259450595665810647045219}{787662783788549761} \) |
\( \bigl[2 a^{5} - 2 a^{4} - 9 a^{3} + 7 a^{2} + 7 a - 2\) , \( -2 a^{5} + 3 a^{4} + 8 a^{3} - 9 a^{2} - 4 a + 3\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 6 a^{2} - 2 a + 1\) , \( 29 a^{5} - 75 a^{4} + 28 a^{3} - 3 a^{2} + 20 a - 13\) , \( 343 a^{5} - 1030 a^{4} + 482 a^{3} + 522 a^{2} - 417 a + 59\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-9a^{3}+7a^{2}+7a-2\right){x}{y}+\left(-a^{5}+2a^{4}+4a^{3}-6a^{2}-2a+1\right){y}={x}^{3}+\left(-2a^{5}+3a^{4}+8a^{3}-9a^{2}-4a+3\right){x}^{2}+\left(29a^{5}-75a^{4}+28a^{3}-3a^{2}+20a-13\right){x}+343a^{5}-1030a^{4}+482a^{3}+522a^{2}-417a+59$ |
| 31.1-a10 |
31.1-a |
$12$ |
$24$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( -31 \) |
$82.86011$ |
$(2a^5-3a^4-8a^3+10a^2+5a-4)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$16$ |
\( 1 \) |
$1$ |
$1025.792884$ |
1.47276 |
\( -\frac{11771614728650068311718789996606}{31} a^{5} + \frac{20672646131967906688095174594552}{31} a^{4} + \frac{52127615514169524635482470593815}{31} a^{3} - \frac{81461266340971407505611370906367}{31} a^{2} - \frac{43408078775695757231287999254039}{31} a + \frac{48272736797749486398912337205132}{31} \) |
\( \bigl[-2 a^{5} + 3 a^{4} + 9 a^{3} - 10 a^{2} - 8 a + 3\) , \( -a^{5} + 5 a^{3} + a^{2} - 5 a - 1\) , \( 0\) , \( 10 a^{5} - 40 a^{4} - 45 a^{3} + 165 a^{2} + 45 a - 104\) , \( -98 a^{5} + 215 a^{4} + 445 a^{3} - 840 a^{2} - 378 a + 495\bigr] \) |
${y}^2+\left(-2a^{5}+3a^{4}+9a^{3}-10a^{2}-8a+3\right){x}{y}={x}^{3}+\left(-a^{5}+5a^{3}+a^{2}-5a-1\right){x}^{2}+\left(10a^{5}-40a^{4}-45a^{3}+165a^{2}+45a-104\right){x}-98a^{5}+215a^{4}+445a^{3}-840a^{2}-378a+495$ |
| 31.1-a11 |
31.1-a |
$12$ |
$24$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( 31^{2} \) |
$82.86011$ |
$(2a^5-3a^4-8a^3+10a^2+5a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1024$ |
\( 2 \) |
$1$ |
$2.003501727$ |
1.47276 |
\( \frac{391232997836344118812955063578726935614}{961} a^{5} - \frac{1146049847494581967103997115183815738335}{961} a^{4} - \frac{499875566564262423437058881855118969349}{961} a^{3} + \frac{3594412435730780139116852441515415592364}{961} a^{2} - \frac{2557922789646965076659228190817527550844}{961} a + \frac{420984754490672117422372247124701363035}{961} \) |
\( \bigl[a^{5} - 5 a^{3} + 4 a + 1\) , \( a^{5} - 5 a^{3} + 5 a + 1\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 7 a^{2} - 2 a + 3\) , \( -780 a^{5} + 1038 a^{4} + 3796 a^{3} - 3603 a^{2} - 3947 a + 909\) , \( -18772 a^{5} + 25124 a^{4} + 91377 a^{3} - 88985 a^{2} - 95239 a + 28271\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+4a+1\right){x}{y}+\left(-a^{5}+2a^{4}+4a^{3}-7a^{2}-2a+3\right){y}={x}^{3}+\left(a^{5}-5a^{3}+5a+1\right){x}^{2}+\left(-780a^{5}+1038a^{4}+3796a^{3}-3603a^{2}-3947a+909\right){x}-18772a^{5}+25124a^{4}+91377a^{3}-88985a^{2}-95239a+28271$ |
| 31.1-a12 |
31.1-a |
$12$ |
$24$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( 31^{6} \) |
$82.86011$ |
$(2a^5-3a^4-8a^3+10a^2+5a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1024$ |
\( 2 \) |
$1$ |
$2.003501727$ |
1.47276 |
\( -\frac{10510572824308508672048934061763533884455273120}{887503681} a^{5} + \frac{3305871471997241704018322895385287159227247726}{887503681} a^{4} + \frac{47614244462683863442287631883194112269531793955}{887503681} a^{3} - \frac{3832115914609593129580786996785582548127284427}{887503681} a^{2} - \frac{27480068985972161720812424402012532444681628853}{887503681} a + \frac{6235982576035498927652588865167121704519444776}{887503681} \) |
\( \bigl[a + 1\) , \( -a^{5} + 5 a^{3} - 3 a + 1\) , \( a^{4} - 3 a^{2} + 1\) , \( -452 a^{5} + 1969 a^{4} - 1949 a^{3} - 1368 a^{2} + 2213 a - 432\) , \( 32265 a^{5} - 121682 a^{4} + 90467 a^{3} + 89084 a^{2} - 96074 a + 17221\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{4}-3a^{2}+1\right){y}={x}^{3}+\left(-a^{5}+5a^{3}-3a+1\right){x}^{2}+\left(-452a^{5}+1969a^{4}-1949a^{3}-1368a^{2}+2213a-432\right){x}+32265a^{5}-121682a^{4}+90467a^{3}+89084a^{2}-96074a+17221$ |
| 31.1-b1 |
31.1-b |
$2$ |
$2$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( - 31^{2} \) |
$82.86011$ |
$(2a^5-3a^4-8a^3+10a^2+5a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.011533825$ |
$44479.43355$ |
2.20967 |
\( -\frac{121782753873715}{961} a^{5} + \frac{463527301865015}{961} a^{4} - \frac{349999328708341}{961} a^{3} - \frac{342242022893993}{961} a^{2} + \frac{374527129960401}{961} a - \frac{67437424076363}{961} \) |
\( \bigl[a^{5} - 5 a^{3} + 4 a + 1\) , \( 3 a^{5} - 4 a^{4} - 13 a^{3} + 13 a^{2} + 11 a - 4\) , \( -a^{5} + 2 a^{4} + 5 a^{3} - 7 a^{2} - 6 a + 3\) , \( -4 a^{5} - 11 a^{4} + 30 a^{3} + 30 a^{2} - 7 a - 3\) , \( 11 a^{5} + 22 a^{4} - 105 a^{3} - 11 a^{2} + 75 a - 16\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+4a+1\right){x}{y}+\left(-a^{5}+2a^{4}+5a^{3}-7a^{2}-6a+3\right){y}={x}^{3}+\left(3a^{5}-4a^{4}-13a^{3}+13a^{2}+11a-4\right){x}^{2}+\left(-4a^{5}-11a^{4}+30a^{3}+30a^{2}-7a-3\right){x}+11a^{5}+22a^{4}-105a^{3}-11a^{2}+75a-16$ |
| 31.1-b2 |
31.1-b |
$2$ |
$2$ |
6.6.485125.1 |
$6$ |
$[6, 0]$ |
31.1 |
\( 31 \) |
\( -31 \) |
$82.86011$ |
$(2a^5-3a^4-8a^3+10a^2+5a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.005766912$ |
$177917.7342$ |
2.20967 |
\( -\frac{1433069}{31} a^{5} + \frac{5349198}{31} a^{4} - \frac{3937183}{31} a^{3} - \frac{3915684}{31} a^{2} + \frac{4225469}{31} a - \frac{762686}{31} \) |
\( \bigl[a^{5} - 5 a^{3} + 4 a + 1\) , \( 3 a^{5} - 4 a^{4} - 13 a^{3} + 13 a^{2} + 11 a - 4\) , \( -a^{5} + 2 a^{4} + 5 a^{3} - 7 a^{2} - 6 a + 3\) , \( 11 a^{5} - 11 a^{4} - 50 a^{3} + 35 a^{2} + 43 a - 13\) , \( 5 a^{5} - 4 a^{4} - 24 a^{3} + 15 a^{2} + 21 a - 6\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+4a+1\right){x}{y}+\left(-a^{5}+2a^{4}+5a^{3}-7a^{2}-6a+3\right){y}={x}^{3}+\left(3a^{5}-4a^{4}-13a^{3}+13a^{2}+11a-4\right){x}^{2}+\left(11a^{5}-11a^{4}-50a^{3}+35a^{2}+43a-13\right){x}+5a^{5}-4a^{4}-24a^{3}+15a^{2}+21a-6$ |
*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.
