| 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 |
| 16.1-a1 |
16.1-a |
$2$ |
$17$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$3.40269$ |
$(2)$ |
0 |
$\Z/17\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$17$ |
17B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$3747.579090$ |
0.481597208 |
\( \frac{63139}{2} a^{3} - \frac{63139}{2} a^{2} - 63139 a - 19975 \) |
\( \bigl[a^{3} - 2 a\) , \( a^{2} - 2 a - 1\) , \( a^{2}\) , \( -a^{3} + a^{2} + a\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}+a^{2}{y}={x}^{3}+\left(a^{2}-2a-1\right){x}^{2}+\left(-a^{3}+a^{2}+a\right){x}$ |
| 16.1-a2 |
16.1-a |
$2$ |
$17$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{68} \) |
$3.40269$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$17$ |
17B.1.3 |
$289$ |
\( 1 \) |
$1$ |
$0.044869902$ |
0.481597208 |
\( -\frac{1823165439649343}{131072} a^{3} + \frac{1823165439649343}{131072} a^{2} + \frac{1823165439649343}{65536} a - \frac{2950374307928381}{131072} \) |
\( \bigl[a^{3} - 2 a\) , \( a^{2} - 2 a - 1\) , \( a^{2}\) , \( -651 a^{3} - 699 a^{2} + 651 a\) , \( -22754 a^{3} - 25330 a^{2} + 18130 a + 8832\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}+a^{2}{y}={x}^{3}+\left(a^{2}-2a-1\right){x}^{2}+\left(-651a^{3}-699a^{2}+651a\right){x}-22754a^{3}-25330a^{2}+18130a+8832$ |
| 25.1-a1 |
25.1-a |
$2$ |
$13$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{26} \) |
$3.59791$ |
$(-2a^3+2a^2+4a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$13$ |
13B.1.2 |
$169$ |
\( 1 \) |
$1$ |
$0.090493666$ |
0.567983715 |
\( -\frac{9401666179616768}{78125} a^{3} + \frac{9401666179616768}{78125} a^{2} + \frac{18803332359233536}{78125} a - \frac{15212221580529664}{78125} \) |
\( \bigl[0\) , \( -a + 1\) , \( a^{2} - a - 1\) , \( -6039 a^{3} + 8759 a^{2} + 13737 a - 12538\) , \( -299268 a^{3} + 440180 a^{2} + 685551 a - 625284\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6039a^{3}+8759a^{2}+13737a-12538\right){x}-299268a^{3}+440180a^{2}+685551a-625284$ |
| 25.1-a2 |
25.1-a |
$2$ |
$13$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{2} \) |
$3.59791$ |
$(-2a^3+2a^2+4a-1)$ |
0 |
$\Z/13\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$13$ |
13B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2584.589597$ |
0.567983715 |
\( \frac{192512}{5} a^{3} - \frac{192512}{5} a^{2} - \frac{385024}{5} a - \frac{118784}{5} \) |
\( \bigl[0\) , \( -a + 1\) , \( a^{2} - a - 1\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 4 a^{3} - 6 a^{2} - 9 a + 8\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(a^{3}-a^{2}-3a+2\right){x}+4a^{3}-6a^{2}-9a+8$ |
| 31.1-a1 |
31.1-a |
$6$ |
$8$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( - 31^{2} \) |
$3.69596$ |
$(a^3-4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$2.037764955$ |
0.605445524 |
\( -\frac{684671267177826448818939504010641}{961} a^{3} + \frac{179630144675804716369884860197999}{961} a^{2} + \frac{2186516236280323395350819631179492}{961} a + \frac{928191236738378773754859996135354}{961} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( a^{3} - a^{2} - a + 1\) , \( 1\) , \( 396 a^{3} - 114 a^{2} - 1262 a - 535\) , \( 5675 a^{3} - 1590 a^{2} - 18077 a - 7642\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+2\right){x}{y}+{y}={x}^{3}+\left(a^{3}-a^{2}-a+1\right){x}^{2}+\left(396a^{3}-114a^{2}-1262a-535\right){x}+5675a^{3}-1590a^{2}-18077a-7642$ |
| 31.1-a2 |
31.1-a |
$6$ |
$8$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( -31 \) |
$3.69596$ |
$(a^3-4a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$260.8339143$ |
0.605445524 |
\( \frac{124454632427233023090075}{31} a^{3} - \frac{183851849860629664577947}{31} a^{2} - \frac{285618764065472969753522}{31} a + \frac{260769042758034501218421}{31} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( a^{3} - a^{2} - a + 1\) , \( 1\) , \( -24 a^{3} + 26 a^{2} + 68 a - 60\) , \( 61 a^{3} - 64 a^{2} - 197 a + 150\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+2\right){x}{y}+{y}={x}^{3}+\left(a^{3}-a^{2}-a+1\right){x}^{2}+\left(-24a^{3}+26a^{2}+68a-60\right){x}+61a^{3}-64a^{2}-197a+150$ |
| 31.1-a3 |
31.1-a |
$6$ |
$8$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( 31^{4} \) |
$3.69596$ |
$(a^3-4a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$32.60423929$ |
0.605445524 |
\( -\frac{419511683908480280709}{923521} a^{3} + \frac{110062957460434799749}{923521} a^{2} + \frac{1339721925491697657614}{923521} a + \frac{568721206322809065061}{923521} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( a^{3} - a^{2} - a + 1\) , \( 1\) , \( 26 a^{3} - 24 a^{2} - 72 a - 30\) , \( 81 a^{3} - 76 a^{2} - 269 a - 102\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+2\right){x}{y}+{y}={x}^{3}+\left(a^{3}-a^{2}-a+1\right){x}^{2}+\left(26a^{3}-24a^{2}-72a-30\right){x}+81a^{3}-76a^{2}-269a-102$ |
| 31.1-a4 |
31.1-a |
$6$ |
$8$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( 31^{2} \) |
$3.69596$ |
$(a^3-4a+1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$521.6678287$ |
0.605445524 |
\( \frac{36738001081029}{961} a^{3} - \frac{54284970454237}{961} a^{2} - \frac{84302445013370}{961} a + \frac{77014952470666}{961} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( a^{3} - a^{2} - a + 1\) , \( 1\) , \( a^{3} + a^{2} - 2 a - 5\) , \( a^{3} - 5 a - 2\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+2\right){x}{y}+{y}={x}^{3}+\left(a^{3}-a^{2}-a+1\right){x}^{2}+\left(a^{3}+a^{2}-2a-5\right){x}+a^{3}-5a-2$ |
| 31.1-a5 |
31.1-a |
$6$ |
$8$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( -31 \) |
$3.69596$ |
$(a^3-4a+1)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1043.335657$ |
0.605445524 |
\( -\frac{3718699}{31} a^{3} + \frac{5432555}{31} a^{2} + \frac{8575846}{31} a - \frac{7570141}{31} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( a^{3} - a^{2} - a + 1\) , \( 1\) , \( a^{3} + a^{2} - 2 a\) , \( a^{3} - a\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+2\right){x}{y}+{y}={x}^{3}+\left(a^{3}-a^{2}-a+1\right){x}^{2}+\left(a^{3}+a^{2}-2a\right){x}+a^{3}-a$ |
| 31.1-a6 |
31.1-a |
$6$ |
$8$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( - 31^{8} \) |
$3.69596$ |
$(a^3-4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$2.037764955$ |
0.605445524 |
\( \frac{206065140764354323915985}{852891037441} a^{3} + \frac{249452633351127967773393}{852891037441} a^{2} - \frac{151495593455929061592036}{852891037441} a - \frac{106721268617817034471018}{852891037441} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( a^{3} - a^{2} - a + 1\) , \( 1\) , \( 56 a^{3} - 334 a^{2} - 2 a + 75\) , \( 107 a^{3} - 3446 a^{2} + 603 a + 1078\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+2\right){x}{y}+{y}={x}^{3}+\left(a^{3}-a^{2}-a+1\right){x}^{2}+\left(56a^{3}-334a^{2}-2a+75\right){x}+107a^{3}-3446a^{2}+603a+1078$ |
| 31.2-a1 |
31.2-a |
$6$ |
$8$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( - 31^{8} \) |
$3.69596$ |
$(a^2-2a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$2.037764955$ |
0.605445524 |
\( \frac{922217602952616201845297}{852891037441} a^{3} - \frac{1377735377068098493534675}{852891037441} a^{2} - \frac{2105069893978011989930528}{852891037441} a + \frac{1975984515916891718526428}{852891037441} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( -a^{3} + a^{2} + a - 1\) , \( 0\) , \( -115 a^{3} + 395 a^{2} + 120 a - 934\) , \( -1763 a^{3} + 4933 a^{2} + 2430 a - 10526\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+2\right){x}{y}={x}^{3}+\left(-a^{3}+a^{2}+a-1\right){x}^{2}+\left(-115a^{3}+395a^{2}+120a-934\right){x}-1763a^{3}+4933a^{2}+2430a-10526$ |
| 31.2-a2 |
31.2-a |
$6$ |
$8$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( 31^{4} \) |
$3.69596$ |
$(a^2-2a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$32.60423929$ |
0.605445524 |
\( -\frac{228261852681788665473}{923521} a^{3} + \frac{537710579129834146433}{923521} a^{2} - \frac{44174852311159765250}{923521} a - \frac{168375141794635762583}{923521} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( -a^{3} + a^{2} + a - 1\) , \( 0\) , \( 5 a^{3} - 5 a^{2} + 10 a - 49\) , \( 26 a^{3} - 50 a^{2} + 56 a - 129\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+2\right){x}{y}={x}^{3}+\left(-a^{3}+a^{2}+a-1\right){x}^{2}+\left(5a^{3}-5a^{2}+10a-49\right){x}+26a^{3}-50a^{2}+56a-129$ |
| 31.2-a3 |
31.2-a |
$6$ |
$8$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( -31 \) |
$3.69596$ |
$(a^2-2a-3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$260.8339143$ |
0.605445524 |
\( \frac{28347915782829458028831}{31} a^{3} + \frac{31049301650567183459041}{31} a^{2} - \frac{19986332354651992484290}{31} a - \frac{13529326186558988306439}{31} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( -a^{3} + a^{2} + a - 1\) , \( 0\) , \( -5 a^{3} + 5 a^{2} - 10 a - 39\) , \( 20 a^{3} + 4 a^{2} + 36 a + 83\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+2\right){x}{y}={x}^{3}+\left(-a^{3}+a^{2}+a-1\right){x}^{2}+\left(-5a^{3}+5a^{2}-10a-39\right){x}+20a^{3}+4a^{2}+36a+83$ |
| 31.2-a4 |
31.2-a |
$6$ |
$8$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( 31^{2} \) |
$3.69596$ |
$(a^2-2a-3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$521.6678287$ |
0.605445524 |
\( \frac{8364588856509}{961} a^{3} + \frac{9182380516699}{961} a^{2} - \frac{5902734861706}{961} a - \frac{3999367873478}{961} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( -a^{3} + a^{2} + a - 1\) , \( 0\) , \( -4\) , \( a^{3} - a^{2} + 2 a - 1\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+2\right){x}{y}={x}^{3}+\left(-a^{3}+a^{2}+a-1\right){x}^{2}-4{x}+a^{3}-a^{2}+2a-1$ |
| 31.2-a5 |
31.2-a |
$6$ |
$8$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( -31 \) |
$3.69596$ |
$(a^2-2a-3)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1043.335657$ |
0.605445524 |
\( -\frac{866395}{31} a^{3} - \frac{847461}{31} a^{2} + \frac{594342}{31} a + \frac{423731}{31} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( -a^{3} + a^{2} + a - 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+2\right){x}{y}={x}^{3}+\left(-a^{3}+a^{2}+a-1\right){x}^{2}+{x}$ |
| 31.2-a6 |
31.2-a |
$6$ |
$8$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( - 31^{2} \) |
$3.69596$ |
$(a^2-2a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$2.037764955$ |
0.605445524 |
\( -\frac{372538687755177683555053524665073}{961} a^{3} + \frac{877579810257199416004108168477715}{961} a^{2} - \frac{72096326414315130602833573828064}{961} a - \frac{274799551345037658328417955957004}{961} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( -a^{3} + a^{2} + a - 1\) , \( 0\) , \( 205 a^{3} - 485 a^{2} + 60 a + 116\) , \( 3195 a^{3} - 7469 a^{2} + 618 a + 2116\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+2\right){x}{y}={x}^{3}+\left(-a^{3}+a^{2}+a-1\right){x}^{2}+\left(205a^{3}-485a^{2}+60a+116\right){x}+3195a^{3}-7469a^{2}+618a+2116$ |
| 41.1-a1 |
41.1-a |
$4$ |
$14$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
41.1 |
\( 41 \) |
\( - 41^{14} \) |
$3.82741$ |
$(2a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.3 |
$49$ |
\( 2 \) |
$1$ |
$0.710843393$ |
0.646801491 |
\( -\frac{810939896619168038925048532608067}{37929227194915558802161} a^{3} + \frac{212752930759282248530045838290319}{37929227194915558802161} a^{2} + \frac{2589791855410129246389009917631159}{37929227194915558802161} a + \frac{1099395124815539388754079429341069}{37929227194915558802161} \) |
\( \bigl[a + 1\) , \( -a^{3} + 2 a^{2} - 3\) , \( a + 1\) , \( 2219 a^{3} - 409 a^{2} - 7390 a - 3741\) , \( 84340 a^{3} - 20755 a^{2} - 271950 a - 120407\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}-3\right){x}^{2}+\left(2219a^{3}-409a^{2}-7390a-3741\right){x}+84340a^{3}-20755a^{2}-271950a-120407$ |
| 41.1-a2 |
41.1-a |
$4$ |
$14$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
41.1 |
\( 41 \) |
\( 41^{7} \) |
$3.82741$ |
$(2a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.3 |
$49$ |
\( 1 \) |
$1$ |
$1.421686787$ |
0.646801491 |
\( \frac{40339934834123038982065}{194754273881} a^{3} + \frac{109012605912848659645570}{194754273881} a^{2} - \frac{45321263640087543078106}{194754273881} a - \frac{42075291893531993359624}{194754273881} \) |
\( \bigl[a + 1\) , \( -a^{3} + 2 a^{2} - 3\) , \( a + 1\) , \( 99 a^{3} - 89 a^{2} - 445 a - 196\) , \( 785 a^{3} - 766 a^{2} - 3686 a - 1645\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}-3\right){x}^{2}+\left(99a^{3}-89a^{2}-445a-196\right){x}+785a^{3}-766a^{2}-3686a-1645$ |
| 41.1-a3 |
41.1-a |
$4$ |
$14$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
41.1 |
\( 41 \) |
\( - 41^{2} \) |
$3.82741$ |
$(2a^2-a-3)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$1706.734988$ |
0.646801491 |
\( \frac{4102114369346}{1681} a^{3} - \frac{5988741927479}{1681} a^{2} - \frac{9370177909896}{1681} a + \frac{8524056894480}{1681} \) |
\( \bigl[a + 1\) , \( -a^{3} + 2 a^{2} - 3\) , \( a + 1\) , \( -6 a^{3} + 16 a^{2} - 41\) , \( 21 a^{3} - 54 a^{2} - 19 a + 127\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}-3\right){x}^{2}+\left(-6a^{3}+16a^{2}-41\right){x}+21a^{3}-54a^{2}-19a+127$ |
| 41.1-a4 |
41.1-a |
$4$ |
$14$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
41.1 |
\( 41 \) |
\( 41 \) |
$3.82741$ |
$(2a^2-a-3)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$3413.469977$ |
0.646801491 |
\( -\frac{1332303}{41} a^{3} + \frac{2252331}{41} a^{2} + \frac{2700811}{41} a - \frac{2683021}{41} \) |
\( \bigl[a + 1\) , \( -a^{3} + 2 a^{2} - 3\) , \( a + 1\) , \( -a^{3} + a^{2} - 1\) , \( -a^{2} + 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}-3\right){x}^{2}+\left(-a^{3}+a^{2}-1\right){x}-a^{2}+3$ |
| 41.2-a1 |
41.2-a |
$4$ |
$14$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
41.2 |
\( 41 \) |
\( 41^{7} \) |
$3.82741$ |
$(a^3-3a^2-a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.3 |
$49$ |
\( 1 \) |
$1$ |
$1.421686787$ |
0.646801491 |
\( \frac{225051081609253272495724}{194754273881} a^{3} - \frac{374403622356224971123359}{194754273881} a^{2} - \frac{485460769246665079877472}{194754273881} a + \frac{590693477122513336036940}{194754273881} \) |
\( \bigl[a^{3} - a^{2} - a + 2\) , \( a^{3} - 4 a\) , \( 1\) , \( -135 a^{3} + 127 a^{2} + 515 a - 400\) , \( -1476 a^{3} + 1408 a^{2} + 5442 a - 4190\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-a+2\right){x}{y}+{y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+\left(-135a^{3}+127a^{2}+515a-400\right){x}-1476a^{3}+1408a^{2}+5442a-4190$ |
| 41.2-a2 |
41.2-a |
$4$ |
$14$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
41.2 |
\( 41 \) |
\( - 41^{2} \) |
$3.82741$ |
$(a^3-3a^2-a+4)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$1706.734988$ |
0.646801491 |
\( \frac{1049537640009}{1681} a^{3} + \frac{837089918124}{1681} a^{2} - \frac{933126108814}{1681} a - \frac{188402509256}{1681} \) |
\( \bigl[a^{3} - a^{2} - a + 2\) , \( a^{3} - 4 a\) , \( 1\) , \( -5 a^{3} - 3 a^{2} + 20 a - 10\) , \( 2 a^{3} + 7 a^{2} - 18 a + 8\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-a+2\right){x}{y}+{y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+\left(-5a^{3}-3a^{2}+20a-10\right){x}+2a^{3}+7a^{2}-18a+8$ |
| 41.2-a3 |
41.2-a |
$4$ |
$14$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
41.2 |
\( 41 \) |
\( 41 \) |
$3.82741$ |
$(a^3-3a^2-a+4)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$3413.469977$ |
0.646801491 |
\( -\frac{376070}{41} a^{3} - \frac{543958}{41} a^{2} + \frac{715935}{41} a + \frac{1033296}{41} \) |
\( \bigl[a^{3} - a^{2} - a + 2\) , \( a^{3} - 4 a\) , \( 1\) , \( 2 a^{2}\) , \( 2 a^{2} - a - 1\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-a+2\right){x}{y}+{y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+2a^{2}{x}+2a^{2}-a-1$ |
| 41.2-a4 |
41.2-a |
$4$ |
$14$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
41.2 |
\( 41 \) |
\( - 41^{14} \) |
$3.82741$ |
$(a^3-3a^2-a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.3 |
$49$ |
\( 2 \) |
$1$ |
$0.710843393$ |
0.646801491 |
\( -\frac{441214800307260660781138374510790}{37929227194915558802161} a^{3} + \frac{1039401766167146451176141068828538}{37929227194915558802161} a^{2} - \frac{85482461557271846976636103393445}{37929227194915558802161} a - \frac{325440676452210604287018495514898}{37929227194915558802161} \) |
\( \bigl[a^{3} - a^{2} - a + 2\) , \( a^{3} - 4 a\) , \( 1\) , \( 1080 a^{3} - 2888 a^{2} + 790 a + 550\) , \( 46346 a^{3} - 112940 a^{2} + 15137 a + 31683\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-a+2\right){x}{y}+{y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+\left(1080a^{3}-2888a^{2}+790a+550\right){x}+46346a^{3}-112940a^{2}+15137a+31683$ |
| 49.1-a1 |
49.1-a |
$4$ |
$10$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{10} \) |
$3.91365$ |
$(a^3-2a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.4[2] |
$25$ |
\( 1 \) |
$1$ |
$3.058324343$ |
0.709895716 |
\( \frac{57614675133880748}{16807} a^{3} + \frac{63106606186270855}{16807} a^{2} - \frac{40615241629974336}{16807} a - \frac{27495042107669572}{16807} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( -a^{2} + 2 a\) , \( 1\) , \( 473 a^{3} - 148 a^{2} - 1509 a - 633\) , \( 7527 a^{3} - 2032 a^{2} - 24084 a - 10214\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+2a\right){x}^{2}+\left(473a^{3}-148a^{2}-1509a-633\right){x}+7527a^{3}-2032a^{2}-24084a-10214$ |
| 49.1-a2 |
49.1-a |
$4$ |
$10$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{20} \) |
$3.91365$ |
$(a^3-2a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.4[2] |
$25$ |
\( 2 \) |
$1$ |
$1.529162171$ |
0.709895716 |
\( -\frac{649366395672402821983442}{282475249} a^{3} + \frac{1529695726182112186121154}{282475249} a^{2} - \frac{125669986007636959256933}{282475249} a - \frac{478998826494857905578142}{282475249} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( -a^{2} + 2 a\) , \( 1\) , \( 568 a^{3} - 388 a^{2} - 1459 a - 558\) , \( 8695 a^{3} - 4402 a^{2} - 24476 a - 9732\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+2a\right){x}^{2}+\left(568a^{3}-388a^{2}-1459a-558\right){x}+8695a^{3}-4402a^{2}-24476a-9732$ |
| 49.1-a3 |
49.1-a |
$4$ |
$10$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{2} \) |
$3.91365$ |
$(a^3-2a-3)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$1911.452714$ |
0.709895716 |
\( -\frac{16107429}{7} a^{3} + \frac{23744838}{7} a^{2} + \frac{37004162}{7} a - 4799736 \) |
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( -a^{2} + 2 a\) , \( 1\) , \( 3 a^{3} + 2 a^{2} - 14 a - 8\) , \( -5 a^{3} + 18 a + 8\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+2a\right){x}^{2}+\left(3a^{3}+2a^{2}-14a-8\right){x}-5a^{3}+18a+8$ |
| 49.1-a4 |
49.1-a |
$4$ |
$10$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{4} \) |
$3.91365$ |
$(a^3-2a-3)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1[2] |
$1$ |
\( 2 \) |
$1$ |
$955.7263573$ |
0.709895716 |
\( \frac{708532203031371}{49} a^{3} - \frac{1046686276650577}{49} a^{2} - \frac{1626055117053453}{49} a + \frac{1484583260292947}{49} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( -a^{2} + 2 a\) , \( 1\) , \( -7 a^{3} + 7 a^{2} + 16 a - 3\) , \( -25 a^{3} + 2 a^{2} + 84 a + 46\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+2a\right){x}^{2}+\left(-7a^{3}+7a^{2}+16a-3\right){x}-25a^{3}+2a^{2}+84a+46$ |
| 49.2-a1 |
49.2-a |
$4$ |
$10$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
49.2 |
\( 7^{2} \) |
\( - 7^{20} \) |
$3.91365$ |
$(a^2+a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.4[2] |
$25$ |
\( 2 \) |
$1$ |
$1.529162171$ |
0.709895716 |
\( -\frac{1193439842515136061069547}{282475249} a^{3} + \frac{313110512005426696931835}{282475249} a^{2} + \frac{3811282462382714725362911}{282475249} a + \frac{1617915718191536947748889}{282475249} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( a^{3} - 4 a + 1\) , \( a^{3} - a^{2} - 2 a + 2\) , \( 427 a^{3} - 605 a^{2} - 535 a - 162\) , \( 6328 a^{3} - 10800 a^{2} - 5249 a + 192\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}+\left(a^{3}-a^{2}-2a+2\right){y}={x}^{3}+\left(a^{3}-4a+1\right){x}^{2}+\left(427a^{3}-605a^{2}-535a-162\right){x}+6328a^{3}-10800a^{2}-5249a+192$ |
| 49.2-a2 |
49.2-a |
$4$ |
$10$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
49.2 |
\( 7^{2} \) |
\( - 7^{4} \) |
$3.91365$ |
$(a^2+a-3)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1[2] |
$1$ |
\( 2 \) |
$1$ |
$955.7263573$ |
0.709895716 |
\( \frac{161387418421454}{49} a^{3} + \frac{176766655197752}{49} a^{2} - \frac{113784125852197}{49} a - \frac{77023745174588}{49} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( a^{3} - 4 a + 1\) , \( a^{3} - a^{2} - 2 a + 2\) , \( -3 a^{3} + 5 a^{2} - 2\) , \( -18 a^{3} + 42 a^{2} - 2 a - 14\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}+\left(a^{3}-a^{2}-2a+2\right){y}={x}^{3}+\left(a^{3}-4a+1\right){x}^{2}+\left(-3a^{3}+5a^{2}-2\right){x}-18a^{3}+42a^{2}-2a-14$ |
| 49.2-a3 |
49.2-a |
$4$ |
$10$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{2} \) |
$3.91365$ |
$(a^2+a-3)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$1911.452714$ |
0.709895716 |
\( -\frac{3680716}{7} a^{3} - \frac{3956693}{7} a^{2} + \frac{2572128}{7} a + 248684 \) |
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( a^{3} - 4 a + 1\) , \( a^{3} - a^{2} - 2 a + 2\) , \( 2 a^{3} - 5 a^{2} + 3\) , \( -a^{3} + 2 a^{2} - 1\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}+\left(a^{3}-a^{2}-2a+2\right){y}={x}^{3}+\left(a^{3}-4a+1\right){x}^{2}+\left(2a^{3}-5a^{2}+3\right){x}-a^{3}+2a^{2}-1$ |
| 49.2-a4 |
49.2-a |
$4$ |
$10$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{10} \) |
$3.91365$ |
$(a^2+a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.4[2] |
$25$ |
\( 1 \) |
$1$ |
$3.058324343$ |
0.709895716 |
\( \frac{252950065091819511}{16807} a^{3} - \frac{373671346411971114}{16807} a^{2} - \frac{82930605545918026}{2401} a + \frac{530004191810724000}{16807} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( a^{3} - 4 a + 1\) , \( a^{3} - a^{2} - 2 a + 2\) , \( 237 a^{3} - 560 a^{2} + 85 a + 103\) , \( 4228 a^{3} - 10047 a^{2} + 1135 a + 2839\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}+\left(a^{3}-a^{2}-2a+2\right){y}={x}^{3}+\left(a^{3}-4a+1\right){x}^{2}+\left(237a^{3}-560a^{2}+85a+103\right){x}+4228a^{3}-10047a^{2}+1135a+2839$ |
| 79.1-a1 |
79.1-a |
$4$ |
$4$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
79.1 |
\( 79 \) |
\( 79 \) |
$4.15443$ |
$(a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$85.17637350$ |
0.790842774 |
\( \frac{280004110320503166938}{79} a^{3} + \frac{306686817831238582645}{79} a^{2} - \frac{197413286152007787011}{79} a - \frac{133634760663491861706}{79} \) |
\( \bigl[a^{3} - 3 a + 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( a^{3} - 3 a\) , \( -124 a^{3} + 83 a^{2} + 217 a - 168\) , \( 39 a^{3} - 1056 a^{2} - 710 a + 1075\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+1\right){x}^{2}+\left(-124a^{3}+83a^{2}+217a-168\right){x}+39a^{3}-1056a^{2}-710a+1075$ |
| 79.1-a2 |
79.1-a |
$4$ |
$4$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
79.1 |
\( 79 \) |
\( - 79^{4} \) |
$4.15443$ |
$(a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$10.64704668$ |
0.790842774 |
\( -\frac{513204288445866284678}{38950081} a^{3} + \frac{134644351474447600325}{38950081} a^{2} + \frac{1638931420426509344717}{38950081} a + \frac{695737629931543622758}{38950081} \) |
\( \bigl[a^{3} - 3 a + 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( a^{3} - 3 a\) , \( 36 a^{3} + 3 a^{2} - 133 a - 98\) , \( 199 a^{3} - 14 a^{2} - 692 a - 419\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+1\right){x}^{2}+\left(36a^{3}+3a^{2}-133a-98\right){x}+199a^{3}-14a^{2}-692a-419$ |
| 79.1-a3 |
79.1-a |
$4$ |
$4$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
79.1 |
\( 79 \) |
\( 79^{2} \) |
$4.15443$ |
$(a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$170.3527470$ |
0.790842774 |
\( \frac{3372210120607}{6241} a^{3} + \frac{3709990772348}{6241} a^{2} - \frac{2347283067085}{6241} a - \frac{1598574828013}{6241} \) |
\( \bigl[a^{3} - 3 a + 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( a^{3} - 3 a\) , \( -4 a^{3} + 3 a^{2} + 2 a - 13\) , \( -3 a^{3} - 13 a^{2} - 9 a + 4\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+1\right){x}^{2}+\left(-4a^{3}+3a^{2}+2a-13\right){x}-3a^{3}-13a^{2}-9a+4$ |
| 79.1-a4 |
79.1-a |
$4$ |
$4$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
79.1 |
\( 79 \) |
\( -79 \) |
$4.15443$ |
$(a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$340.7054940$ |
0.790842774 |
\( \frac{573246}{79} a^{3} + \frac{587751}{79} a^{2} - \frac{519859}{79} a - \frac{318547}{79} \) |
\( \bigl[a^{3} - 3 a + 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( a^{3} - 3 a\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( a^{3} - 2 a^{2} - 3 a + 2\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+1\right){x}^{2}+\left(a^{3}-2a^{2}-3a+2\right){x}+a^{3}-2a^{2}-3a+2$ |
| 79.2-a1 |
79.2-a |
$4$ |
$4$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
79.2 |
\( 79 \) |
\( 79 \) |
$4.15443$ |
$(-3a^3+4a^2+5a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$85.17637350$ |
0.790842774 |
\( \frac{1229289972961243463386}{79} a^{3} - \frac{1815980901112985212969}{79} a^{2} - \frac{2821174880411485473637}{79} a + \frac{2575723886432473683491}{79} \) |
\( \bigl[a^{3} - 3 a\) , \( a^{3} - 2 a^{2} - a + 3\) , \( a^{3} - 3 a + 1\) , \( -195 a^{3} + 234 a^{2} + 421 a - 359\) , \( -1610 a^{3} + 2626 a^{2} + 3852 a - 3624\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-a+3\right){x}^{2}+\left(-195a^{3}+234a^{2}+421a-359\right){x}-1610a^{3}+2626a^{2}+3852a-3624$ |
| 79.2-a2 |
79.2-a |
$4$ |
$4$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
79.2 |
\( 79 \) |
\( 79^{2} \) |
$4.15443$ |
$(-3a^3+4a^2+5a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$170.3527470$ |
0.790842774 |
\( \frac{14851548187691}{6241} a^{3} - \frac{21933749080646}{6241} a^{2} - \frac{34100233549511}{6241} a + \frac{31127365917936}{6241} \) |
\( \bigl[a^{3} - 3 a\) , \( a^{3} - 2 a^{2} - a + 3\) , \( a^{3} - 3 a + 1\) , \( -10 a^{3} + 9 a^{2} + 26 a - 19\) , \( -34 a^{3} + 49 a^{2} + 83 a - 74\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-a+3\right){x}^{2}+\left(-10a^{3}+9a^{2}+26a-19\right){x}-34a^{3}+49a^{2}+83a-74$ |
| 79.2-a3 |
79.2-a |
$4$ |
$4$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
79.2 |
\( 79 \) |
\( -79 \) |
$4.15443$ |
$(-3a^3+4a^2+5a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$340.7054940$ |
0.790842774 |
\( \frac{2360876}{79} a^{3} - \frac{3521873}{79} a^{2} - \frac{5348385}{79} a + \frac{4952074}{79} \) |
\( \bigl[a^{3} - 3 a\) , \( a^{3} - 2 a^{2} - a + 3\) , \( a^{3} - 3 a + 1\) , \( -a^{2} + a + 1\) , \( -a^{3} + a^{2} + 3 a - 2\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-a+3\right){x}^{2}+\left(-a^{2}+a+1\right){x}-a^{3}+a^{2}+3a-2$ |
| 79.2-a4 |
79.2-a |
$4$ |
$4$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
79.2 |
\( 79 \) |
\( - 79^{4} \) |
$4.15443$ |
$(-3a^3+4a^2+5a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$10.64704668$ |
0.790842774 |
\( -\frac{279241381882508193670}{38950081} a^{3} + \frac{657801318853926878023}{38950081} a^{2} - \frac{54040079769760388021}{38950081} a - \frac{205979274419354339293}{38950081} \) |
\( \bigl[a^{3} - 3 a\) , \( a^{3} - 2 a^{2} - a + 3\) , \( a^{3} - 3 a + 1\) , \( 15 a^{3} - 56 a^{2} + 31 a + 1\) , \( 90 a^{3} - 276 a^{2} + 114 a + 28\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-a+3\right){x}^{2}+\left(15a^{3}-56a^{2}+31a+1\right){x}+90a^{3}-276a^{2}+114a+28$ |
| 89.1-a1 |
89.1-a |
$4$ |
$6$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
89.1 |
\( 89 \) |
\( - 89^{2} \) |
$4.21678$ |
$(-2a^3+5a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$390.5355223$ |
0.805784732 |
\( \frac{27644790669914081}{7921} a^{3} - \frac{40838543328263983}{7921} a^{2} - \frac{63443769227304147}{7921} a + \frac{57923964030045892}{7921} \) |
\( \bigl[a^{3} - 3 a\) , \( a^{3} - 3 a + 1\) , \( a^{2}\) , \( -10 a^{3} + 16 a^{2} + 25 a - 25\) , \( 19 a^{3} - 30 a^{2} - 38 a + 38\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+a^{2}{y}={x}^{3}+\left(a^{3}-3a+1\right){x}^{2}+\left(-10a^{3}+16a^{2}+25a-25\right){x}+19a^{3}-30a^{2}-38a+38$ |
| 89.1-a2 |
89.1-a |
$4$ |
$6$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
89.1 |
\( 89 \) |
\( 89 \) |
$4.21678$ |
$(-2a^3+5a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$781.0710447$ |
0.805784732 |
\( \frac{100842659}{89} a^{3} - \frac{147757920}{89} a^{2} - \frac{230679948}{89} a + \frac{210082231}{89} \) |
\( \bigl[a^{3} - 3 a\) , \( a^{3} - 3 a + 1\) , \( a^{2}\) , \( a^{2}\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+a^{2}{y}={x}^{3}+\left(a^{3}-3a+1\right){x}^{2}+a^{2}{x}$ |
| 89.1-a3 |
89.1-a |
$4$ |
$6$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
89.1 |
\( 89 \) |
\( 89^{3} \) |
$4.21678$ |
$(-2a^3+5a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$9.642852404$ |
0.805784732 |
\( \frac{14708200401504137868}{704969} a^{3} + \frac{16109789617602422544}{704969} a^{2} - \frac{10369823372478176308}{704969} a - \frac{7019630806488219407}{704969} \) |
\( \bigl[a^{3} - 3 a\) , \( a^{3} - 3 a + 1\) , \( a^{2}\) , \( -5 a^{3} - 19 a^{2} + 10 a + 5\) , \( -40 a^{3} - 95 a^{2} + 47 a + 31\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+a^{2}{y}={x}^{3}+\left(a^{3}-3a+1\right){x}^{2}+\left(-5a^{3}-19a^{2}+10a+5\right){x}-40a^{3}-95a^{2}+47a+31$ |
| 89.1-a4 |
89.1-a |
$4$ |
$6$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
89.1 |
\( 89 \) |
\( - 89^{6} \) |
$4.21678$ |
$(-2a^3+5a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$4.821426202$ |
0.805784732 |
\( -\frac{101672510628391532828120426}{496981290961} a^{3} + \frac{239507317407110136025004820}{496981290961} a^{2} - \frac{19676384011560149188326968}{496981290961} a - \frac{74997740941951418606146221}{496981290961} \) |
\( \bigl[a^{3} - 3 a\) , \( a^{3} - 3 a + 1\) , \( a^{2}\) , \( 70 a^{3} - 189 a^{2} + 25 a + 30\) , \( 801 a^{3} - 2028 a^{2} + 111 a + 647\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+a^{2}{y}={x}^{3}+\left(a^{3}-3a+1\right){x}^{2}+\left(70a^{3}-189a^{2}+25a+30\right){x}+801a^{3}-2028a^{2}+111a+647$ |
| 89.2-a1 |
89.2-a |
$4$ |
$6$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
89.2 |
\( 89 \) |
\( - 89^{6} \) |
$4.21678$ |
$(-2a^3+a^2+7a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$4.821426202$ |
0.805784732 |
\( -\frac{186859109118016144475803852}{496981290961} a^{3} + \frac{49024302339297541278919458}{496981290961} a^{2} + \frac{596739623504375503796175524}{496981290961} a + \frac{253320080904579779336823535}{496981290961} \) |
\( \bigl[a^{3} - 2 a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} - a^{2} - 2 a + 1\) , \( 1072 a^{3} - 335 a^{2} - 3329 a - 1409\) , \( 24371 a^{3} - 6724 a^{2} - 77278 a - 32742\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a^{3}-a^{2}-2a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(1072a^{3}-335a^{2}-3329a-1409\right){x}+24371a^{3}-6724a^{2}-77278a-32742$ |
| 89.2-a2 |
89.2-a |
$4$ |
$6$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
89.2 |
\( 89 \) |
\( 89^{3} \) |
$4.21678$ |
$(-2a^3+a^2+7a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$9.642852404$ |
0.805784732 |
\( \frac{64572767851140797708}{704969} a^{3} - \frac{95390757870247358120}{704969} a^{2} - \frac{148192113132811694844}{704969} a + \frac{135298906700468121669}{704969} \) |
\( \bigl[a^{3} - 2 a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} - a^{2} - 2 a + 1\) , \( 62 a^{3} - 10 a^{2} - 199 a - 99\) , \( 369 a^{3} - 90 a^{2} - 1170 a - 539\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a^{3}-a^{2}-2a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(62a^{3}-10a^{2}-199a-99\right){x}+369a^{3}-90a^{2}-1170a-539$ |
| 89.2-a3 |
89.2-a |
$4$ |
$6$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
89.2 |
\( 89 \) |
\( - 89^{2} \) |
$4.21678$ |
$(-2a^3+a^2+7a-2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$390.5355223$ |
0.805784732 |
\( \frac{6296850124088194}{7921} a^{3} + \frac{6896902534261708}{7921} a^{2} - \frac{4439512360700403}{7921} a - \frac{3005234490829701}{7921} \) |
\( \bigl[a^{3} - 2 a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} - a^{2} - 2 a + 1\) , \( 17 a^{3} - 10 a^{2} - 44 a - 14\) , \( 31 a^{3} - 3 a^{2} - 106 a - 46\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a^{3}-a^{2}-2a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(17a^{3}-10a^{2}-44a-14\right){x}+31a^{3}-3a^{2}-106a-46$ |
| 89.2-a4 |
89.2-a |
$4$ |
$6$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
89.2 |
\( 89 \) |
\( 89 \) |
$4.21678$ |
$(-2a^3+a^2+7a-2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$781.0710447$ |
0.805784732 |
\( \frac{24932768}{89} a^{3} + \frac{21982493}{89} a^{2} - \frac{20870906}{89} a - \frac{6573443}{89} \) |
\( \bigl[a^{3} - 2 a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} - a^{2} - 2 a + 1\) , \( 2 a^{3} - 4 a + 1\) , \( 2 a^{3} + a^{2} - 5 a - 2\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a^{3}-a^{2}-2a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(2a^{3}-4a+1\right){x}+2a^{3}+a^{2}-5a-2$ |
| 109.1-a1 |
109.1-a |
$2$ |
$11$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
109.1 |
\( 109 \) |
\( 109^{11} \) |
$4.32500$ |
$(-a^3+a^2+5a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.2 |
$121$ |
\( 1 \) |
$1$ |
$0.188236531$ |
0.845902442 |
\( \frac{16235216636009362328759362787732}{25804264053054077850709} a^{3} - \frac{4260010497864756660724731056719}{25804264053054077850709} a^{2} - \frac{51855684642834574989082645270777}{25804264053054077850709} a - \frac{22019771839812368650729782793234}{25804264053054077850709} \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{3} + 2 a^{2} + a - 3\) , \( a^{2} - a\) , \( 540 a^{3} - 71 a^{2} - 1805 a - 989\) , \( 10516 a^{3} - 2406 a^{2} - 33972 a - 15480\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{2}-a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+a-3\right){x}^{2}+\left(540a^{3}-71a^{2}-1805a-989\right){x}+10516a^{3}-2406a^{2}-33972a-15480$ |
| 109.1-a2 |
109.1-a |
$2$ |
$11$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
109.1 |
\( 109 \) |
\( 109 \) |
$4.32500$ |
$(-a^3+a^2+5a)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2755.971058$ |
0.845902442 |
\( \frac{3718291}{109} a^{3} - \frac{9007348}{109} a^{2} + \frac{1282551}{109} a + \frac{2463928}{109} \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{3} + 2 a^{2} + a - 3\) , \( a^{2} - a\) , \( -a^{2} + 1\) , \( -a^{2} + a + 1\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{2}-a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+a-3\right){x}^{2}+\left(-a^{2}+1\right){x}-a^{2}+a+1$ |
*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.
