| 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 |
| 43.3-a1 |
43.3-a |
$6$ |
$8$ |
6.6.905177.1 |
$6$ |
$[6, 0]$ |
43.3 |
\( 43 \) |
\( - 43^{8} \) |
$116.31285$ |
$(-a^5+7a^3-a^2-8a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$273.5819904$ |
2.30044 |
\( \frac{3406213225180447232907260}{11688200277601} a^{5} - \frac{6962830214805161351471360}{11688200277601} a^{4} - \frac{16573221433629042835142139}{11688200277601} a^{3} + \frac{47960978848778752831185762}{11688200277601} a^{2} - \frac{26235290819869803508572383}{11688200277601} a - \frac{3262166902052129678810404}{11688200277601} \) |
\( \bigl[2 a^{5} + a^{4} - 13 a^{3} - a^{2} + 16 a + 2\) , \( 3 a^{5} + a^{4} - 20 a^{3} + 24 a + 4\) , \( a^{5} + a^{4} - 6 a^{3} - 2 a^{2} + 7 a\) , \( 13 a^{5} - 2 a^{4} - 83 a^{3} + 11 a^{2} + 104 a + 11\) , \( 21 a^{5} - 19 a^{4} - 95 a^{3} + 33 a^{2} + 111 a + 11\bigr] \) |
${y}^2+\left(2a^{5}+a^{4}-13a^{3}-a^{2}+16a+2\right){x}{y}+\left(a^{5}+a^{4}-6a^{3}-2a^{2}+7a\right){y}={x}^{3}+\left(3a^{5}+a^{4}-20a^{3}+24a+4\right){x}^{2}+\left(13a^{5}-2a^{4}-83a^{3}+11a^{2}+104a+11\right){x}+21a^{5}-19a^{4}-95a^{3}+33a^{2}+111a+11$ |
| 43.3-a2 |
43.3-a |
$6$ |
$8$ |
6.6.905177.1 |
$6$ |
$[6, 0]$ |
43.3 |
\( 43 \) |
\( 43^{2} \) |
$116.31285$ |
$(-a^5+7a^3-a^2-8a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$17509.24739$ |
2.30044 |
\( -\frac{186743634412}{1849} a^{5} - \frac{1089177918}{1849} a^{4} + \frac{1387590358407}{1849} a^{3} - \frac{89789267076}{1849} a^{2} - \frac{1536345558627}{1849} a - \frac{157129430426}{1849} \) |
\( \bigl[2 a^{5} - 13 a^{3} + 5 a^{2} + 13 a - 2\) , \( -1\) , \( 2 a^{5} + a^{4} - 12 a^{3} + 13 a + 1\) , \( -76 a^{5} - 21 a^{4} + 504 a^{3} - 40 a^{2} - 577 a - 60\) , \( -334 a^{5} - 95 a^{4} + 2215 a^{3} - 162 a^{2} - 2541 a - 260\bigr] \) |
${y}^2+\left(2a^{5}-13a^{3}+5a^{2}+13a-2\right){x}{y}+\left(2a^{5}+a^{4}-12a^{3}+13a+1\right){y}={x}^{3}-{x}^{2}+\left(-76a^{5}-21a^{4}+504a^{3}-40a^{2}-577a-60\right){x}-334a^{5}-95a^{4}+2215a^{3}-162a^{2}-2541a-260$ |
| 43.3-a3 |
43.3-a |
$6$ |
$8$ |
6.6.905177.1 |
$6$ |
$[6, 0]$ |
43.3 |
\( 43 \) |
\( 43^{4} \) |
$116.31285$ |
$(-a^5+7a^3-a^2-8a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$17509.24739$ |
2.30044 |
\( -\frac{2490198020699}{3418801} a^{5} + \frac{2361670776245}{3418801} a^{4} + \frac{17898027845635}{3418801} a^{3} - \frac{22308302643766}{3418801} a^{2} - \frac{20072706519767}{3418801} a + \frac{26941274571745}{3418801} \) |
\( \bigl[2 a^{5} + a^{4} - 13 a^{3} - a^{2} + 16 a + 2\) , \( 3 a^{5} + a^{4} - 20 a^{3} + 24 a + 4\) , \( a^{5} + a^{4} - 6 a^{3} - 2 a^{2} + 7 a\) , \( 13 a^{5} + 3 a^{4} - 88 a^{3} + 6 a^{2} + 104 a + 11\) , \( 12 a^{5} + 4 a^{4} - 78 a^{3} + 3 a^{2} + 89 a + 9\bigr] \) |
${y}^2+\left(2a^{5}+a^{4}-13a^{3}-a^{2}+16a+2\right){x}{y}+\left(a^{5}+a^{4}-6a^{3}-2a^{2}+7a\right){y}={x}^{3}+\left(3a^{5}+a^{4}-20a^{3}+24a+4\right){x}^{2}+\left(13a^{5}+3a^{4}-88a^{3}+6a^{2}+104a+11\right){x}+12a^{5}+4a^{4}-78a^{3}+3a^{2}+89a+9$ |
| 43.3-a4 |
43.3-a |
$6$ |
$8$ |
6.6.905177.1 |
$6$ |
$[6, 0]$ |
43.3 |
\( 43 \) |
\( -43 \) |
$116.31285$ |
$(-a^5+7a^3-a^2-8a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$8754.623695$ |
2.30044 |
\( \frac{69796344781787}{43} a^{5} + \frac{19770982289703}{43} a^{4} - \frac{463203062951736}{43} a^{3} + \frac{33754233470488}{43} a^{2} + \frac{531890184951534}{43} a + \frac{54389607200804}{43} \) |
\( \bigl[2 a^{5} + a^{4} - 12 a^{3} + 12 a + 1\) , \( a^{5} + a^{4} - 7 a^{3} - 4 a^{2} + 9 a + 2\) , \( 2 a^{5} + a^{4} - 12 a^{3} + 12 a + 1\) , \( -7 a^{5} + 46 a^{3} - 26 a^{2} - 43 a + 25\) , \( -7 a^{5} + 9 a^{4} + 46 a^{3} - 71 a^{2} - 44 a + 76\bigr] \) |
${y}^2+\left(2a^{5}+a^{4}-12a^{3}+12a+1\right){x}{y}+\left(2a^{5}+a^{4}-12a^{3}+12a+1\right){y}={x}^{3}+\left(a^{5}+a^{4}-7a^{3}-4a^{2}+9a+2\right){x}^{2}+\left(-7a^{5}+46a^{3}-26a^{2}-43a+25\right){x}-7a^{5}+9a^{4}+46a^{3}-71a^{2}-44a+76$ |
| 43.3-a5 |
43.3-a |
$6$ |
$8$ |
6.6.905177.1 |
$6$ |
$[6, 0]$ |
43.3 |
\( 43 \) |
\( - 43^{2} \) |
$116.31285$ |
$(-a^5+7a^3-a^2-8a-3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$17509.24739$ |
2.30044 |
\( -\frac{12917248269178553}{1849} a^{5} + \frac{14259644336097429}{1849} a^{4} + \frac{88938836446013470}{1849} a^{3} - \frac{125498003585609358}{1849} a^{2} - \frac{77378640090922546}{1849} a + \frac{124296636281239242}{1849} \) |
\( \bigl[a^{5} + a^{4} - 5 a^{3} - a^{2} + 5 a - 2\) , \( a^{5} + a^{4} - 5 a^{3} - a^{2} + 5 a - 3\) , \( -a^{5} + 7 a^{3} - a^{2} - 8 a - 2\) , \( 19 a^{5} + 21 a^{4} - 100 a^{3} - 38 a^{2} + 108 a + 11\) , \( 50 a^{5} + 55 a^{4} - 263 a^{3} - 100 a^{2} + 285 a + 30\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-5a^{3}-a^{2}+5a-2\right){x}{y}+\left(-a^{5}+7a^{3}-a^{2}-8a-2\right){y}={x}^{3}+\left(a^{5}+a^{4}-5a^{3}-a^{2}+5a-3\right){x}^{2}+\left(19a^{5}+21a^{4}-100a^{3}-38a^{2}+108a+11\right){x}+50a^{5}+55a^{4}-263a^{3}-100a^{2}+285a+30$ |
| 43.3-a6 |
43.3-a |
$6$ |
$8$ |
6.6.905177.1 |
$6$ |
$[6, 0]$ |
43.3 |
\( 43 \) |
\( -43 \) |
$116.31285$ |
$(-a^5+7a^3-a^2-8a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$1$ |
$547.1639809$ |
2.30044 |
\( \frac{1173569754551973325}{43} a^{5} + \frac{2266579903080684169}{43} a^{4} - \frac{3306457199116643064}{43} a^{3} - \frac{3287184324570861224}{43} a^{2} + \frac{1541500712896424618}{43} a + \frac{191737203111697412}{43} \) |
\( \bigl[2 a^{5} - 13 a^{3} + 5 a^{2} + 13 a - 2\) , \( -1\) , \( 2 a^{5} + a^{4} - 12 a^{3} + 13 a + 1\) , \( -21 a^{5} - a^{4} + 154 a^{3} - 25 a^{2} - 217 a - 30\) , \( -345 a^{5} - 75 a^{4} + 2328 a^{3} - 257 a^{2} - 2743 a - 293\bigr] \) |
${y}^2+\left(2a^{5}-13a^{3}+5a^{2}+13a-2\right){x}{y}+\left(2a^{5}+a^{4}-12a^{3}+13a+1\right){y}={x}^{3}-{x}^{2}+\left(-21a^{5}-a^{4}+154a^{3}-25a^{2}-217a-30\right){x}-345a^{5}-75a^{4}+2328a^{3}-257a^{2}-2743a-293$ |
| 43.3-b1 |
43.3-b |
$2$ |
$2$ |
6.6.905177.1 |
$6$ |
$[6, 0]$ |
43.3 |
\( 43 \) |
\( 43^{3} \) |
$116.31285$ |
$(-a^5+7a^3-a^2-8a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$7102.595059$ |
1.86634 |
\( -\frac{145441004546799}{79507} a^{5} - \frac{71120357824962}{79507} a^{4} + \frac{912143341749074}{79507} a^{3} + \frac{49190950251620}{79507} a^{2} - \frac{944554435943153}{79507} a - \frac{97467565841434}{79507} \) |
\( \bigl[a^{4} + a^{3} - 4 a^{2} - a + 1\) , \( -a^{4} + 5 a^{2} - 2 a\) , \( a^{2} - 3\) , \( 3 a^{5} - 2 a^{4} - 15 a^{3} + 15 a^{2} + 7 a - 3\) , \( -32 a^{5} - 26 a^{4} + 160 a^{3} + 37 a^{2} - 156 a - 15\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-4a^{2}-a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{4}+5a^{2}-2a\right){x}^{2}+\left(3a^{5}-2a^{4}-15a^{3}+15a^{2}+7a-3\right){x}-32a^{5}-26a^{4}+160a^{3}+37a^{2}-156a-15$ |
| 43.3-b2 |
43.3-b |
$2$ |
$2$ |
6.6.905177.1 |
$6$ |
$[6, 0]$ |
43.3 |
\( 43 \) |
\( - 43^{6} \) |
$116.31285$ |
$(-a^5+7a^3-a^2-8a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3551.297529$ |
1.86634 |
\( \frac{318403691331473}{6321363049} a^{5} + \frac{173816603925064}{6321363049} a^{4} - \frac{1948660970376257}{6321363049} a^{3} - \frac{119733970035159}{6321363049} a^{2} + \frac{2012913934869055}{6321363049} a + \frac{202362364150543}{6321363049} \) |
\( \bigl[-a^{5} + 7 a^{3} - a^{2} - 7 a - 1\) , \( -a^{5} - a^{4} + 6 a^{3} + 2 a^{2} - 8 a\) , \( a^{3} + 2 a^{2} - 2 a - 3\) , \( -65 a^{5} - 59 a^{4} + 344 a^{3} + 70 a^{2} - 331 a - 35\) , \( -535 a^{5} - 487 a^{4} + 2817 a^{3} + 569 a^{2} - 2667 a - 282\bigr] \) |
${y}^2+\left(-a^{5}+7a^{3}-a^{2}-7a-1\right){x}{y}+\left(a^{3}+2a^{2}-2a-3\right){y}={x}^{3}+\left(-a^{5}-a^{4}+6a^{3}+2a^{2}-8a\right){x}^{2}+\left(-65a^{5}-59a^{4}+344a^{3}+70a^{2}-331a-35\right){x}-535a^{5}-487a^{4}+2817a^{3}+569a^{2}-2667a-282$ |
| 43.3-c1 |
43.3-c |
$4$ |
$4$ |
6.6.905177.1 |
$6$ |
$[6, 0]$ |
43.3 |
\( 43 \) |
\( -43 \) |
$116.31285$ |
$(-a^5+7a^3-a^2-8a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$1862.964613$ |
1.95811 |
\( -\frac{6192886500544956335412}{43} a^{5} - \frac{3029555474725010992458}{43} a^{4} + \frac{38838593880728994328498}{43} a^{3} + \frac{2102426891231803835805}{43} a^{2} - \frac{40219273494687139702655}{43} a - \frac{4158534459891333793843}{43} \) |
\( \bigl[2 a^{5} + a^{4} - 13 a^{3} - a^{2} + 15 a + 2\) , \( a^{5} - a^{4} - 8 a^{3} + 6 a^{2} + 8 a - 1\) , \( 2 a^{5} + a^{4} - 12 a^{3} + 13 a + 1\) , \( -28 a^{5} - 17 a^{4} + 137 a^{3} - 31 a^{2} - 89 a - 8\) , \( 36 a^{5} + 166 a^{4} - 31 a^{3} - 502 a^{2} + 151 a + 21\bigr] \) |
${y}^2+\left(2a^{5}+a^{4}-13a^{3}-a^{2}+15a+2\right){x}{y}+\left(2a^{5}+a^{4}-12a^{3}+13a+1\right){y}={x}^{3}+\left(a^{5}-a^{4}-8a^{3}+6a^{2}+8a-1\right){x}^{2}+\left(-28a^{5}-17a^{4}+137a^{3}-31a^{2}-89a-8\right){x}+36a^{5}+166a^{4}-31a^{3}-502a^{2}+151a+21$ |
| 43.3-c2 |
43.3-c |
$4$ |
$4$ |
6.6.905177.1 |
$6$ |
$[6, 0]$ |
43.3 |
\( 43 \) |
\( 43^{2} \) |
$116.31285$ |
$(-a^5+7a^3-a^2-8a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$14903.71690$ |
1.95811 |
\( -\frac{18795092322872}{1849} a^{5} - \frac{9197015644591}{1849} a^{4} + \frac{117868536456430}{1849} a^{3} + \frac{6390280749779}{1849} a^{2} - \frac{122048957749258}{1849} a - \frac{12618508676415}{1849} \) |
\( \bigl[2 a^{5} + a^{4} - 13 a^{3} - a^{2} + 15 a + 2\) , \( a^{5} - a^{4} - 8 a^{3} + 6 a^{2} + 8 a - 1\) , \( 2 a^{5} + a^{4} - 12 a^{3} + 13 a + 1\) , \( -18 a^{5} - 17 a^{4} + 92 a^{3} + 19 a^{2} - 84 a - 8\) , \( -59 a^{5} - 51 a^{4} + 314 a^{3} + 53 a^{2} - 295 a - 31\bigr] \) |
${y}^2+\left(2a^{5}+a^{4}-13a^{3}-a^{2}+15a+2\right){x}{y}+\left(2a^{5}+a^{4}-12a^{3}+13a+1\right){y}={x}^{3}+\left(a^{5}-a^{4}-8a^{3}+6a^{2}+8a-1\right){x}^{2}+\left(-18a^{5}-17a^{4}+92a^{3}+19a^{2}-84a-8\right){x}-59a^{5}-51a^{4}+314a^{3}+53a^{2}-295a-31$ |
| 43.3-c3 |
43.3-c |
$4$ |
$4$ |
6.6.905177.1 |
$6$ |
$[6, 0]$ |
43.3 |
\( 43 \) |
\( - 43^{4} \) |
$116.31285$ |
$(-a^5+7a^3-a^2-8a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3725.929226$ |
1.95811 |
\( \frac{3649320162593979}{3418801} a^{5} + \frac{3305647721589223}{3418801} a^{4} - \frac{19245197647346057}{3418801} a^{3} - \frac{3833979657134919}{3418801} a^{2} + \frac{18238238681182310}{3418801} a + \frac{1914832530089513}{3418801} \) |
\( \bigl[a^{4} + a^{3} - 4 a^{2} - a + 1\) , \( -a^{5} + 7 a^{3} - a^{2} - 9 a - 3\) , \( a^{5} + a^{4} - 6 a^{3} - 3 a^{2} + 8 a + 3\) , \( 3 a^{5} - 2 a^{4} - 21 a^{3} + 19 a^{2} + 22 a - 16\) , \( 7 a^{5} - 9 a^{4} - 47 a^{3} + 73 a^{2} + 40 a - 73\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-4a^{2}-a+1\right){x}{y}+\left(a^{5}+a^{4}-6a^{3}-3a^{2}+8a+3\right){y}={x}^{3}+\left(-a^{5}+7a^{3}-a^{2}-9a-3\right){x}^{2}+\left(3a^{5}-2a^{4}-21a^{3}+19a^{2}+22a-16\right){x}+7a^{5}-9a^{4}-47a^{3}+73a^{2}+40a-73$ |
| 43.3-c4 |
43.3-c |
$4$ |
$4$ |
6.6.905177.1 |
$6$ |
$[6, 0]$ |
43.3 |
\( 43 \) |
\( 43 \) |
$116.31285$ |
$(-a^5+7a^3-a^2-8a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$7451.858453$ |
1.95811 |
\( -\frac{1322746521861}{43} a^{5} + \frac{1460469666576}{43} a^{4} + \frac{9106508382145}{43} a^{3} - \frac{12850539162726}{43} a^{2} - \frac{7922671045286}{43} a + \frac{12727123139301}{43} \) |
\( \bigl[a^{5} + a^{4} - 6 a^{3} - 3 a^{2} + 8 a + 3\) , \( -a^{4} + 7 a^{2} - 2 a - 7\) , \( a^{5} + a^{4} - 6 a^{3} - 3 a^{2} + 8 a + 3\) , \( 13 a^{5} + 8 a^{4} - 80 a^{3} - 14 a^{2} + 83 a + 16\) , \( -23 a^{5} - 12 a^{4} + 144 a^{3} + 13 a^{2} - 150 a - 22\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-6a^{3}-3a^{2}+8a+3\right){x}{y}+\left(a^{5}+a^{4}-6a^{3}-3a^{2}+8a+3\right){y}={x}^{3}+\left(-a^{4}+7a^{2}-2a-7\right){x}^{2}+\left(13a^{5}+8a^{4}-80a^{3}-14a^{2}+83a+16\right){x}-23a^{5}-12a^{4}+144a^{3}+13a^{2}-150a-22$ |
| 43.3-d1 |
43.3-d |
$4$ |
$4$ |
6.6.905177.1 |
$6$ |
$[6, 0]$ |
43.3 |
\( 43 \) |
\( -43 \) |
$116.31285$ |
$(-a^5+7a^3-a^2-8a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.061012198$ |
$1673.517249$ |
2.79947 |
\( -\frac{6192886500544956335412}{43} a^{5} - \frac{3029555474725010992458}{43} a^{4} + \frac{38838593880728994328498}{43} a^{3} + \frac{2102426891231803835805}{43} a^{2} - \frac{40219273494687139702655}{43} a - \frac{4158534459891333793843}{43} \) |
\( \bigl[2 a^{5} - 13 a^{3} + 5 a^{2} + 14 a - 2\) , \( a^{5} - 6 a^{3} + 4 a^{2} + 4 a - 4\) , \( a^{5} - 7 a^{3} + 2 a^{2} + 9 a\) , \( -14 a^{5} + a^{4} + 77 a^{3} - 43 a^{2} - 27 a - 24\) , \( 14 a^{5} - 34 a^{4} - 68 a^{3} + 223 a^{2} - 130 a - 13\bigr] \) |
${y}^2+\left(2a^{5}-13a^{3}+5a^{2}+14a-2\right){x}{y}+\left(a^{5}-7a^{3}+2a^{2}+9a\right){y}={x}^{3}+\left(a^{5}-6a^{3}+4a^{2}+4a-4\right){x}^{2}+\left(-14a^{5}+a^{4}+77a^{3}-43a^{2}-27a-24\right){x}+14a^{5}-34a^{4}-68a^{3}+223a^{2}-130a-13$ |
| 43.3-d2 |
43.3-d |
$4$ |
$4$ |
6.6.905177.1 |
$6$ |
$[6, 0]$ |
43.3 |
\( 43 \) |
\( 43^{2} \) |
$116.31285$ |
$(-a^5+7a^3-a^2-8a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.530506099$ |
$6694.068998$ |
2.79947 |
\( -\frac{18795092322872}{1849} a^{5} - \frac{9197015644591}{1849} a^{4} + \frac{117868536456430}{1849} a^{3} + \frac{6390280749779}{1849} a^{2} - \frac{122048957749258}{1849} a - \frac{12618508676415}{1849} \) |
\( \bigl[2 a^{5} - 13 a^{3} + 5 a^{2} + 14 a - 2\) , \( a^{5} - 6 a^{3} + 4 a^{2} + 4 a - 4\) , \( a^{5} - 7 a^{3} + 2 a^{2} + 9 a\) , \( -4 a^{5} - 4 a^{4} + 22 a^{3} + 12 a^{2} - 22 a - 19\) , \( -10 a^{5} - 11 a^{4} + 52 a^{3} + 23 a^{2} - 50 a - 22\bigr] \) |
${y}^2+\left(2a^{5}-13a^{3}+5a^{2}+14a-2\right){x}{y}+\left(a^{5}-7a^{3}+2a^{2}+9a\right){y}={x}^{3}+\left(a^{5}-6a^{3}+4a^{2}+4a-4\right){x}^{2}+\left(-4a^{5}-4a^{4}+22a^{3}+12a^{2}-22a-19\right){x}-10a^{5}-11a^{4}+52a^{3}+23a^{2}-50a-22$ |
| 43.3-d3 |
43.3-d |
$4$ |
$4$ |
6.6.905177.1 |
$6$ |
$[6, 0]$ |
43.3 |
\( 43 \) |
\( - 43^{4} \) |
$116.31285$ |
$(-a^5+7a^3-a^2-8a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.265253049$ |
$1673.517249$ |
2.79947 |
\( \frac{3649320162593979}{3418801} a^{5} + \frac{3305647721589223}{3418801} a^{4} - \frac{19245197647346057}{3418801} a^{3} - \frac{3833979657134919}{3418801} a^{2} + \frac{18238238681182310}{3418801} a + \frac{1914832530089513}{3418801} \) |
\( \bigl[a^{2} - 2\) , \( a^{4} + a^{3} - 4 a^{2} - 2 a\) , \( 2 a^{5} + a^{4} - 12 a^{3} + 12 a\) , \( 11 a^{5} + 6 a^{4} - 69 a^{3} - 4 a^{2} + 68 a + 6\) , \( 28 a^{5} + 11 a^{4} - 182 a^{3} + 2 a^{2} + 200 a + 20\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(2a^{5}+a^{4}-12a^{3}+12a\right){y}={x}^{3}+\left(a^{4}+a^{3}-4a^{2}-2a\right){x}^{2}+\left(11a^{5}+6a^{4}-69a^{3}-4a^{2}+68a+6\right){x}+28a^{5}+11a^{4}-182a^{3}+2a^{2}+200a+20$ |
| 43.3-d4 |
43.3-d |
$4$ |
$4$ |
6.6.905177.1 |
$6$ |
$[6, 0]$ |
43.3 |
\( 43 \) |
\( 43 \) |
$116.31285$ |
$(-a^5+7a^3-a^2-8a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.061012198$ |
$1673.517249$ |
2.79947 |
\( -\frac{1322746521861}{43} a^{5} + \frac{1460469666576}{43} a^{4} + \frac{9106508382145}{43} a^{3} - \frac{12850539162726}{43} a^{2} - \frac{7922671045286}{43} a + \frac{12727123139301}{43} \) |
\( \bigl[3 a^{5} + a^{4} - 19 a^{3} + 2 a^{2} + 20 a\) , \( -2 a^{5} - a^{4} + 12 a^{3} + a^{2} - 13 a - 2\) , \( a^{4} + a^{3} - 4 a^{2} + 1\) , \( -13 a^{5} - 7 a^{4} + 86 a^{3} + 20 a^{2} - 110 a - 46\) , \( 98 a^{5} + 19 a^{4} - 650 a^{3} + 113 a^{2} + 722 a - 13\bigr] \) |
${y}^2+\left(3a^{5}+a^{4}-19a^{3}+2a^{2}+20a\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}+1\right){y}={x}^{3}+\left(-2a^{5}-a^{4}+12a^{3}+a^{2}-13a-2\right){x}^{2}+\left(-13a^{5}-7a^{4}+86a^{3}+20a^{2}-110a-46\right){x}+98a^{5}+19a^{4}-650a^{3}+113a^{2}+722a-13$ |
| 43.3-e1 |
43.3-e |
$2$ |
$2$ |
6.6.905177.1 |
$6$ |
$[6, 0]$ |
43.3 |
\( 43 \) |
\( 43^{3} \) |
$116.31285$ |
$(-a^5+7a^3-a^2-8a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.034461589$ |
$18120.10903$ |
2.95353 |
\( -\frac{145441004546799}{79507} a^{5} - \frac{71120357824962}{79507} a^{4} + \frac{912143341749074}{79507} a^{3} + \frac{49190950251620}{79507} a^{2} - \frac{944554435943153}{79507} a - \frac{97467565841434}{79507} \) |
\( \bigl[a^{5} + a^{4} - 5 a^{3} - a^{2} + 4 a - 2\) , \( -2 a^{5} - a^{4} + 12 a^{3} + a^{2} - 12 a - 2\) , \( a^{5} - 6 a^{3} + 3 a^{2} + 6 a - 2\) , \( 5 a^{5} - 2 a^{4} - 34 a^{3} + 27 a^{2} + 34 a - 24\) , \( -3 a^{5} + 5 a^{4} + 22 a^{3} - 38 a^{2} - 19 a + 37\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-5a^{3}-a^{2}+4a-2\right){x}{y}+\left(a^{5}-6a^{3}+3a^{2}+6a-2\right){y}={x}^{3}+\left(-2a^{5}-a^{4}+12a^{3}+a^{2}-12a-2\right){x}^{2}+\left(5a^{5}-2a^{4}-34a^{3}+27a^{2}+34a-24\right){x}-3a^{5}+5a^{4}+22a^{3}-38a^{2}-19a+37$ |
| 43.3-e2 |
43.3-e |
$2$ |
$2$ |
6.6.905177.1 |
$6$ |
$[6, 0]$ |
43.3 |
\( 43 \) |
\( - 43^{6} \) |
$116.31285$ |
$(-a^5+7a^3-a^2-8a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.017230794$ |
$18120.10903$ |
2.95353 |
\( \frac{318403691331473}{6321363049} a^{5} + \frac{173816603925064}{6321363049} a^{4} - \frac{1948660970376257}{6321363049} a^{3} - \frac{119733970035159}{6321363049} a^{2} + \frac{2012913934869055}{6321363049} a + \frac{202362364150543}{6321363049} \) |
\( \bigl[a^{5} - 6 a^{3} + 4 a^{2} + 6 a - 4\) , \( 2 a^{5} - 13 a^{3} + 5 a^{2} + 13 a - 4\) , \( 2 a^{5} + a^{4} - 12 a^{3} + 12 a\) , \( -9 a^{5} - 9 a^{4} + 48 a^{3} + 17 a^{2} - 47 a - 14\) , \( -47 a^{5} - 41 a^{4} + 249 a^{3} + 40 a^{2} - 236 a - 15\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}+4a^{2}+6a-4\right){x}{y}+\left(2a^{5}+a^{4}-12a^{3}+12a\right){y}={x}^{3}+\left(2a^{5}-13a^{3}+5a^{2}+13a-4\right){x}^{2}+\left(-9a^{5}-9a^{4}+48a^{3}+17a^{2}-47a-14\right){x}-47a^{5}-41a^{4}+249a^{3}+40a^{2}-236a-15$ |
| 43.3-f1 |
43.3-f |
$6$ |
$8$ |
6.6.905177.1 |
$6$ |
$[6, 0]$ |
43.3 |
\( 43 \) |
\( - 43^{8} \) |
$116.31285$ |
$(-a^5+7a^3-a^2-8a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.029144025$ |
$6571.604378$ |
2.41566 |
\( \frac{3406213225180447232907260}{11688200277601} a^{5} - \frac{6962830214805161351471360}{11688200277601} a^{4} - \frac{16573221433629042835142139}{11688200277601} a^{3} + \frac{47960978848778752831185762}{11688200277601} a^{2} - \frac{26235290819869803508572383}{11688200277601} a - \frac{3262166902052129678810404}{11688200277601} \) |
\( \bigl[a^{5} + a^{4} - 6 a^{3} - 2 a^{2} + 8 a\) , \( a^{5} + a^{4} - 6 a^{3} - 3 a^{2} + 7 a + 3\) , \( a^{5} - 7 a^{3} + 2 a^{2} + 8 a - 1\) , \( 31 a^{5} + 9 a^{4} - 206 a^{3} + 16 a^{2} + 247 a + 24\) , \( -64 a^{5} - 46 a^{4} + 377 a^{3} + 84 a^{2} - 339 a - 36\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-6a^{3}-2a^{2}+8a\right){x}{y}+\left(a^{5}-7a^{3}+2a^{2}+8a-1\right){y}={x}^{3}+\left(a^{5}+a^{4}-6a^{3}-3a^{2}+7a+3\right){x}^{2}+\left(31a^{5}+9a^{4}-206a^{3}+16a^{2}+247a+24\right){x}-64a^{5}-46a^{4}+377a^{3}+84a^{2}-339a-36$ |
| 43.3-f2 |
43.3-f |
$6$ |
$8$ |
6.6.905177.1 |
$6$ |
$[6, 0]$ |
43.3 |
\( 43 \) |
\( 43^{2} \) |
$116.31285$ |
$(-a^5+7a^3-a^2-8a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.029144025$ |
$105145.6700$ |
2.41566 |
\( -\frac{186743634412}{1849} a^{5} - \frac{1089177918}{1849} a^{4} + \frac{1387590358407}{1849} a^{3} - \frac{89789267076}{1849} a^{2} - \frac{1536345558627}{1849} a - \frac{157129430426}{1849} \) |
\( \bigl[-a^{5} + 7 a^{3} - a^{2} - 8 a - 1\) , \( -2 a^{5} - a^{4} + 12 a^{3} - 12 a - 1\) , \( a^{2} - 2\) , \( -2 a^{5} + 8 a^{4} + 8 a^{3} - 51 a^{2} + 35 a + 4\) , \( 7 a^{5} - 17 a^{4} - 33 a^{3} + 113 a^{2} - 65 a - 9\bigr] \) |
${y}^2+\left(-a^{5}+7a^{3}-a^{2}-8a-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-2a^{5}-a^{4}+12a^{3}-12a-1\right){x}^{2}+\left(-2a^{5}+8a^{4}+8a^{3}-51a^{2}+35a+4\right){x}+7a^{5}-17a^{4}-33a^{3}+113a^{2}-65a-9$ |
| 43.3-f3 |
43.3-f |
$6$ |
$8$ |
6.6.905177.1 |
$6$ |
$[6, 0]$ |
43.3 |
\( 43 \) |
\( 43^{4} \) |
$116.31285$ |
$(-a^5+7a^3-a^2-8a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.014572012$ |
$105145.6700$ |
2.41566 |
\( -\frac{2490198020699}{3418801} a^{5} + \frac{2361670776245}{3418801} a^{4} + \frac{17898027845635}{3418801} a^{3} - \frac{22308302643766}{3418801} a^{2} - \frac{20072706519767}{3418801} a + \frac{26941274571745}{3418801} \) |
\( \bigl[a^{5} + a^{4} - 6 a^{3} - 2 a^{2} + 8 a\) , \( a^{5} + a^{4} - 6 a^{3} - 3 a^{2} + 7 a + 3\) , \( a^{5} - 7 a^{3} + 2 a^{2} + 8 a - 1\) , \( 11 a^{5} + 9 a^{4} - 61 a^{3} - 14 a^{2} + 52 a + 4\) , \( -32 a^{5} - 16 a^{4} + 201 a^{3} + 15 a^{2} - 205 a - 22\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-6a^{3}-2a^{2}+8a\right){x}{y}+\left(a^{5}-7a^{3}+2a^{2}+8a-1\right){y}={x}^{3}+\left(a^{5}+a^{4}-6a^{3}-3a^{2}+7a+3\right){x}^{2}+\left(11a^{5}+9a^{4}-61a^{3}-14a^{2}+52a+4\right){x}-32a^{5}-16a^{4}+201a^{3}+15a^{2}-205a-22$ |
| 43.3-f4 |
43.3-f |
$6$ |
$8$ |
6.6.905177.1 |
$6$ |
$[6, 0]$ |
43.3 |
\( 43 \) |
\( -43 \) |
$116.31285$ |
$(-a^5+7a^3-a^2-8a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.058288050$ |
$26286.41751$ |
2.41566 |
\( \frac{69796344781787}{43} a^{5} + \frac{19770982289703}{43} a^{4} - \frac{463203062951736}{43} a^{3} + \frac{33754233470488}{43} a^{2} + \frac{531890184951534}{43} a + \frac{54389607200804}{43} \) |
\( \bigl[2 a^{5} + a^{4} - 12 a^{3} + a^{2} + 12 a - 3\) , \( -a^{5} + a^{4} + 8 a^{3} - 6 a^{2} - 8 a + 2\) , \( 2 a^{5} + a^{4} - 13 a^{3} - a^{2} + 16 a + 2\) , \( 16 a^{5} + 14 a^{4} - 93 a^{3} - 32 a^{2} + 99 a + 29\) , \( -3 a^{5} + 5 a^{4} + 29 a^{3} - 22 a^{2} - 31 a + 12\bigr] \) |
${y}^2+\left(2a^{5}+a^{4}-12a^{3}+a^{2}+12a-3\right){x}{y}+\left(2a^{5}+a^{4}-13a^{3}-a^{2}+16a+2\right){y}={x}^{3}+\left(-a^{5}+a^{4}+8a^{3}-6a^{2}-8a+2\right){x}^{2}+\left(16a^{5}+14a^{4}-93a^{3}-32a^{2}+99a+29\right){x}-3a^{5}+5a^{4}+29a^{3}-22a^{2}-31a+12$ |
| 43.3-f5 |
43.3-f |
$6$ |
$8$ |
6.6.905177.1 |
$6$ |
$[6, 0]$ |
43.3 |
\( 43 \) |
\( - 43^{2} \) |
$116.31285$ |
$(-a^5+7a^3-a^2-8a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.029144025$ |
$26286.41751$ |
2.41566 |
\( -\frac{12917248269178553}{1849} a^{5} + \frac{14259644336097429}{1849} a^{4} + \frac{88938836446013470}{1849} a^{3} - \frac{125498003585609358}{1849} a^{2} - \frac{77378640090922546}{1849} a + \frac{124296636281239242}{1849} \) |
\( \bigl[a^{5} + a^{4} - 6 a^{3} - 2 a^{2} + 7 a - 1\) , \( -2 a^{5} - a^{4} + 13 a^{3} + 2 a^{2} - 15 a - 4\) , \( a^{5} + a^{4} - 6 a^{3} - 2 a^{2} + 8 a\) , \( -11 a^{5} - 5 a^{4} + 71 a^{3} + 6 a^{2} - 80 a - 21\) , \( -15 a^{5} - a^{4} + 99 a^{3} - 30 a^{2} - 107 a + 14\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-6a^{3}-2a^{2}+7a-1\right){x}{y}+\left(a^{5}+a^{4}-6a^{3}-2a^{2}+8a\right){y}={x}^{3}+\left(-2a^{5}-a^{4}+13a^{3}+2a^{2}-15a-4\right){x}^{2}+\left(-11a^{5}-5a^{4}+71a^{3}+6a^{2}-80a-21\right){x}-15a^{5}-a^{4}+99a^{3}-30a^{2}-107a+14$ |
| 43.3-f6 |
43.3-f |
$6$ |
$8$ |
6.6.905177.1 |
$6$ |
$[6, 0]$ |
43.3 |
\( 43 \) |
\( -43 \) |
$116.31285$ |
$(-a^5+7a^3-a^2-8a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$0.058288050$ |
$6571.604378$ |
2.41566 |
\( \frac{1173569754551973325}{43} a^{5} + \frac{2266579903080684169}{43} a^{4} - \frac{3306457199116643064}{43} a^{3} - \frac{3287184324570861224}{43} a^{2} + \frac{1541500712896424618}{43} a + \frac{191737203111697412}{43} \) |
\( \bigl[2 a^{5} + a^{4} - 12 a^{3} + 13 a + 1\) , \( 3 a^{5} + a^{4} - 19 a^{3} + a^{2} + 19 a + 2\) , \( a + 1\) , \( -43 a^{5} - 38 a^{4} + 232 a^{3} + 48 a^{2} - 232 a - 26\) , \( 158 a^{5} + 139 a^{4} - 834 a^{3} - 149 a^{2} + 784 a + 81\bigr] \) |
${y}^2+\left(2a^{5}+a^{4}-12a^{3}+13a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(3a^{5}+a^{4}-19a^{3}+a^{2}+19a+2\right){x}^{2}+\left(-43a^{5}-38a^{4}+232a^{3}+48a^{2}-232a-26\right){x}+158a^{5}+139a^{4}-834a^{3}-149a^{2}+784a+81$ |
*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.
