| 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 |
| 25.3-a1 |
25.3-a |
$4$ |
$6$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{9} \) |
$8.86354$ |
$(-a^3+a^2+4a-3), (a^3+2a^2-3a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$33.21697500$ |
2.253441329 |
\( \frac{145001676583808}{125} a^{3} + \frac{311602782283904}{125} a^{2} - \frac{345389063626496}{125} a - \frac{742227233987392}{125} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 4\) , \( a^{3} + a^{2} - 4 a - 5\) , \( a^{2} + a - 4\) , \( -5 a^{3} - 15 a^{2} + 6 a + 30\) , \( -27 a^{3} - 136 a^{2} + 31 a + 426\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-5\right){x}^{2}+\left(-5a^{3}-15a^{2}+6a+30\right){x}-27a^{3}-136a^{2}+31a+426$ |
| 25.3-a2 |
25.3-a |
$4$ |
$6$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{9} \) |
$8.86354$ |
$(-a^3+a^2+4a-3), (a^3+2a^2-3a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$33.21697500$ |
2.253441329 |
\( -\frac{145001676583808}{125} a^{3} + \frac{311602782283904}{125} a^{2} + \frac{345389063626496}{125} a - \frac{742227233987392}{125} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 4\) , \( -a^{3} + a^{2} + 3 a - 5\) , \( a^{2} + a - 4\) , \( 4 a^{3} - 15 a^{2} - 3 a + 30\) , \( 26 a^{3} - 136 a^{2} - 27 a + 426\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-5\right){x}^{2}+\left(4a^{3}-15a^{2}-3a+30\right){x}+26a^{3}-136a^{2}-27a+426$ |
| 25.3-a3 |
25.3-a |
$4$ |
$6$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{3} \) |
$8.86354$ |
$(-a^3+a^2+4a-3), (a^3+2a^2-3a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$298.9527750$ |
2.253441329 |
\( -\frac{43136}{5} a^{3} - \frac{59264}{5} a^{2} + \frac{226048}{5} a + \frac{331456}{5} \) |
\( \bigl[a^{3} - 4 a + 1\) , \( a^{3} + a^{2} - 5 a - 3\) , \( a^{2} + a - 4\) , \( a^{3} - 7 a^{2} - 7 a + 29\) , \( -4 a^{2} - 3 a + 12\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-3\right){x}^{2}+\left(a^{3}-7a^{2}-7a+29\right){x}-4a^{2}-3a+12$ |
| 25.3-a4 |
25.3-a |
$4$ |
$6$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{3} \) |
$8.86354$ |
$(-a^3+a^2+4a-3), (a^3+2a^2-3a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$298.9527750$ |
2.253441329 |
\( \frac{43136}{5} a^{3} - \frac{59264}{5} a^{2} - \frac{226048}{5} a + \frac{331456}{5} \) |
\( \bigl[a^{3} - 4 a + 1\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a^{3} + a^{2} - 3 a - 3\) , \( 2 a^{3} - 6 a + 1\) , \( a^{3} - 3 a\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-3\right){x}^{2}+\left(2a^{3}-6a+1\right){x}+a^{3}-3a$ |
| 25.3-b1 |
25.3-b |
$4$ |
$6$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{3} \) |
$8.86354$ |
$(-a^3+a^2+4a-3), (a^3+2a^2-3a-5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$955.0275239$ |
0.799865646 |
\( -\frac{43136}{5} a^{3} - \frac{59264}{5} a^{2} + \frac{226048}{5} a + \frac{331456}{5} \) |
\( \bigl[a^{2} + a - 3\) , \( a^{2} + a - 5\) , \( a^{3} - 4 a\) , \( a^{3} - 4 a + 3\) , \( -1\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(a^{3}-4a+3\right){x}-1$ |
| 25.3-b2 |
25.3-b |
$4$ |
$6$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{9} \) |
$8.86354$ |
$(-a^3+a^2+4a-3), (a^3+2a^2-3a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$11.79046325$ |
0.799865646 |
\( \frac{145001676583808}{125} a^{3} + \frac{311602782283904}{125} a^{2} - \frac{345389063626496}{125} a - \frac{742227233987392}{125} \) |
\( \bigl[a^{2} + a - 3\) , \( a^{2} + a - 5\) , \( a^{3} - 4 a\) , \( -19 a^{3} - 45 a^{2} + 41 a + 108\) , \( -162 a^{3} - 327 a^{2} + 397 a + 755\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(-19a^{3}-45a^{2}+41a+108\right){x}-162a^{3}-327a^{2}+397a+755$ |
| 25.3-b3 |
25.3-b |
$4$ |
$6$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{3} \) |
$8.86354$ |
$(-a^3+a^2+4a-3), (a^3+2a^2-3a-5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$955.0275239$ |
0.799865646 |
\( \frac{43136}{5} a^{3} - \frac{59264}{5} a^{2} - \frac{226048}{5} a + \frac{331456}{5} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{3} + a^{2} + 5 a - 5\) , \( a^{2} + a - 4\) , \( a^{3} - 2 a^{2} - 4 a + 8\) , \( -a^{3} + a^{2} + 5 a - 5\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-5\right){x}^{2}+\left(a^{3}-2a^{2}-4a+8\right){x}-a^{3}+a^{2}+5a-5$ |
| 25.3-b4 |
25.3-b |
$4$ |
$6$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{9} \) |
$8.86354$ |
$(-a^3+a^2+4a-3), (a^3+2a^2-3a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$11.79046325$ |
0.799865646 |
\( -\frac{145001676583808}{125} a^{3} + \frac{311602782283904}{125} a^{2} + \frac{345389063626496}{125} a - \frac{742227233987392}{125} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{3} + a^{2} + 5 a - 5\) , \( a^{2} + a - 4\) , \( 21 a^{3} - 47 a^{2} - 49 a + 113\) , \( 116 a^{3} - 231 a^{2} - 287 a + 531\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-5\right){x}^{2}+\left(21a^{3}-47a^{2}-49a+113\right){x}+116a^{3}-231a^{2}-287a+531$ |
| 31.1-a1 |
31.1-a |
$1$ |
$1$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( 31^{7} \) |
$9.10511$ |
$(-a^3+a^2+4a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$155.2018111$ |
2.339755338 |
\( \frac{20658244006503}{27512614111} a^{3} + \frac{47471524533857}{27512614111} a^{2} - \frac{114350909406398}{27512614111} a - \frac{152350807490055}{27512614111} \) |
\( \bigl[1\) , \( -a^{2} + a + 4\) , \( 0\) , \( -9 a^{3} + 13 a^{2} + 42 a - 59\) , \( 11 a^{3} - 17 a^{2} - 51 a + 80\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-9a^{3}+13a^{2}+42a-59\right){x}+11a^{3}-17a^{2}-51a+80$ |
| 31.1-b1 |
31.1-b |
$1$ |
$1$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( 31 \) |
$9.10511$ |
$(-a^3+a^2+4a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$106.8964377$ |
1.611524434 |
\( \frac{206255355828299}{31} a^{3} - \frac{318326661270219}{31} a^{2} - \frac{952494243687014}{31} a + \frac{1470043341319301}{31} \) |
\( \bigl[a^{3} - 3 a + 1\) , \( a^{3} - a^{2} - 4 a + 5\) , \( a^{3} - 4 a + 1\) , \( -11 a^{3} - 20 a^{2} + 28 a + 43\) , \( -83 a^{3} - 150 a^{2} + 215 a + 331\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+5\right){x}^{2}+\left(-11a^{3}-20a^{2}+28a+43\right){x}-83a^{3}-150a^{2}+215a+331$ |
| 31.1-c1 |
31.1-c |
$4$ |
$4$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( -31 \) |
$9.10511$ |
$(-a^3+a^2+4a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.075403558$ |
$1762.101780$ |
2.003071688 |
\( -\frac{155772}{31} a^{3} - \frac{267325}{31} a^{2} + \frac{634876}{31} a + \frac{1052962}{31} \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{3} - a^{2} + 4 a + 4\) , \( a^{3} - 4 a\) , \( -3 a^{2} + 12\) , \( -30 a^{3} + 64 a^{2} + 72 a - 153\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+4\right){x}^{2}+\left(-3a^{2}+12\right){x}-30a^{3}+64a^{2}+72a-153$ |
| 31.1-c2 |
31.1-c |
$4$ |
$4$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( -31 \) |
$9.10511$ |
$(-a^3+a^2+4a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.301614233$ |
$440.5254452$ |
2.003071688 |
\( \frac{77286524488566078}{31} a^{3} + \frac{166085782662265724}{31} a^{2} - \frac{184093874850639127}{31} a - \frac{395610688650363197}{31} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 3\) , \( a^{3} + a^{2} - 5 a - 3\) , \( a^{3} - 3 a + 1\) , \( 1705 a^{3} + 2619 a^{2} - 7917 a - 12187\) , \( -77155 a^{3} - 119042 a^{2} + 356436 a + 550022\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-3\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-3\right){x}^{2}+\left(1705a^{3}+2619a^{2}-7917a-12187\right){x}-77155a^{3}-119042a^{2}+356436a+550022$ |
| 31.1-c3 |
31.1-c |
$4$ |
$4$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( 31^{2} \) |
$9.10511$ |
$(-a^3+a^2+4a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.150807116$ |
$1762.101780$ |
2.003071688 |
\( -\frac{77272583940}{961} a^{3} - \frac{109867494715}{961} a^{2} + \frac{391445107350}{961} a + \frac{581776625313}{961} \) |
\( \bigl[a^{2} - 3\) , \( a^{3} - a^{2} - 5 a + 4\) , \( a\) , \( -207 a^{3} + 313 a^{2} + 973 a - 1484\) , \( -3221 a^{3} + 4986 a^{2} + 14820 a - 22909\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-a^{2}-5a+4\right){x}^{2}+\left(-207a^{3}+313a^{2}+973a-1484\right){x}-3221a^{3}+4986a^{2}+14820a-22909$ |
| 31.1-c4 |
31.1-c |
$4$ |
$4$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( 31^{4} \) |
$9.10511$ |
$(-a^3+a^2+4a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.075403558$ |
$440.5254452$ |
2.003071688 |
\( -\frac{59370852200354013489666}{923521} a^{3} - \frac{91630712350575600915204}{923521} a^{2} + \frac{274176613402283668981641}{923521} a + \frac{423153744048330031118195}{923521} \) |
\( \bigl[a^{3} - 4 a\) , \( a^{3} + a^{2} - 5 a - 4\) , \( a^{3} + a^{2} - 4 a - 4\) , \( -79 a^{3} - 151 a^{2} + 198 a + 339\) , \( 713 a^{3} + 1513 a^{2} - 1708 a - 3582\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{3}+a^{2}-4a-4\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-4\right){x}^{2}+\left(-79a^{3}-151a^{2}+198a+339\right){x}+713a^{3}+1513a^{2}-1708a-3582$ |
| 31.1-d1 |
31.1-d |
$4$ |
$4$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( -31 \) |
$9.10511$ |
$(-a^3+a^2+4a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1515.810669$ |
1.428231603 |
\( -\frac{155772}{31} a^{3} - \frac{267325}{31} a^{2} + \frac{634876}{31} a + \frac{1052962}{31} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 4\) , \( a^{3} - 5 a + 1\) , \( a\) , \( a^{3} - 3 a^{2} - 5 a + 13\) , \( -6 a^{3} + 14 a^{2} + 12 a - 32\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-4\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-5a+1\right){x}^{2}+\left(a^{3}-3a^{2}-5a+13\right){x}-6a^{3}+14a^{2}+12a-32$ |
| 31.1-d2 |
31.1-d |
$4$ |
$4$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( -31 \) |
$9.10511$ |
$(-a^3+a^2+4a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$378.9526672$ |
1.428231603 |
\( \frac{77286524488566078}{31} a^{3} + \frac{166085782662265724}{31} a^{2} - \frac{184093874850639127}{31} a - \frac{395610688650363197}{31} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{2} + a - 5\) , \( a^{2} + a - 3\) , \( 607 a^{3} + 903 a^{2} - 2920 a - 4421\) , \( 18357 a^{3} + 28564 a^{2} - 83921 a - 130076\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(607a^{3}+903a^{2}-2920a-4421\right){x}+18357a^{3}+28564a^{2}-83921a-130076$ |
| 31.1-d3 |
31.1-d |
$4$ |
$4$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( 31^{4} \) |
$9.10511$ |
$(-a^3+a^2+4a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$47.36908341$ |
1.428231603 |
\( -\frac{59370852200354013489666}{923521} a^{3} - \frac{91630712350575600915204}{923521} a^{2} + \frac{274176613402283668981641}{923521} a + \frac{423153744048330031118195}{923521} \) |
\( \bigl[a^{2} - 3\) , \( a^{3} - 3 a\) , \( a^{3} - 4 a + 1\) , \( -41 a^{3} - 33 a^{2} + 126 a + 19\) , \( 73 a^{3} + 375 a^{2} - 47 a - 1109\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(a^{3}-3a\right){x}^{2}+\left(-41a^{3}-33a^{2}+126a+19\right){x}+73a^{3}+375a^{2}-47a-1109$ |
| 31.1-d4 |
31.1-d |
$4$ |
$4$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( 31^{2} \) |
$9.10511$ |
$(-a^3+a^2+4a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$757.9053345$ |
1.428231603 |
\( -\frac{77272583940}{961} a^{3} - \frac{109867494715}{961} a^{2} + \frac{391445107350}{961} a + \frac{581776625313}{961} \) |
\( \bigl[a^{3} - 4 a\) , \( -a^{3} + a^{2} + 4 a - 5\) , \( a^{2} - 3\) , \( -61 a^{3} + 81 a^{2} + 328 a - 475\) , \( 651 a^{3} - 942 a^{2} - 3238 a + 4848\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-5\right){x}^{2}+\left(-61a^{3}+81a^{2}+328a-475\right){x}+651a^{3}-942a^{2}-3238a+4848$ |
| 31.1-e1 |
31.1-e |
$1$ |
$1$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( 31 \) |
$9.10511$ |
$(-a^3+a^2+4a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.195376744$ |
$161.8086715$ |
1.906374917 |
\( \frac{206255355828299}{31} a^{3} - \frac{318326661270219}{31} a^{2} - \frac{952494243687014}{31} a + \frac{1470043341319301}{31} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 3\) , \( -a^{2} + a + 5\) , \( a^{3} - 3 a\) , \( -29 a^{3} - 60 a^{2} + 73 a + 143\) , \( -302 a^{3} - 652 a^{2} + 719 a + 1556\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-3\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(-29a^{3}-60a^{2}+73a+143\right){x}-302a^{3}-652a^{2}+719a+1556$ |
| 31.1-f1 |
31.1-f |
$1$ |
$1$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( 31^{7} \) |
$9.10511$ |
$(-a^3+a^2+4a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 7 \) |
$0.008173367$ |
$374.2505338$ |
1.291204819 |
\( \frac{20658244006503}{27512614111} a^{3} + \frac{47471524533857}{27512614111} a^{2} - \frac{114350909406398}{27512614111} a - \frac{152350807490055}{27512614111} \) |
\( \bigl[a^{3} - 3 a\) , \( a^{3} - a^{2} - 3 a + 4\) , \( a^{3} - 3 a\) , \( -a^{3} + 4 a^{2} + 9 a - 20\) , \( -5 a^{3} + 12 a^{2} + 25 a - 49\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+4\right){x}^{2}+\left(-a^{3}+4a^{2}+9a-20\right){x}-5a^{3}+12a^{2}+25a-49$ |
| 31.2-a1 |
31.2-a |
$1$ |
$1$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( 31^{7} \) |
$9.10511$ |
$(a^3+a^2-4a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$155.2018111$ |
2.339755338 |
\( -\frac{20658244006503}{27512614111} a^{3} + \frac{47471524533857}{27512614111} a^{2} + \frac{114350909406398}{27512614111} a - \frac{152350807490055}{27512614111} \) |
\( \bigl[1\) , \( -a^{2} - a + 4\) , \( 0\) , \( 9 a^{3} + 13 a^{2} - 42 a - 59\) , \( -11 a^{3} - 17 a^{2} + 51 a + 80\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(9a^{3}+13a^{2}-42a-59\right){x}-11a^{3}-17a^{2}+51a+80$ |
| 31.2-b1 |
31.2-b |
$1$ |
$1$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( 31 \) |
$9.10511$ |
$(a^3+a^2-4a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$106.8964377$ |
1.611524434 |
\( -\frac{206255355828299}{31} a^{3} - \frac{318326661270219}{31} a^{2} + \frac{952494243687014}{31} a + \frac{1470043341319301}{31} \) |
\( \bigl[a^{3} - 3 a + 1\) , \( a^{3} - a^{2} - 5 a + 5\) , \( a^{2} - 3\) , \( 16 a^{3} - 23 a^{2} - 49 a + 56\) , \( 66 a^{3} - 130 a^{2} - 167 a + 307\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a+5\right){x}^{2}+\left(16a^{3}-23a^{2}-49a+56\right){x}+66a^{3}-130a^{2}-167a+307$ |
| 31.2-c1 |
31.2-c |
$4$ |
$4$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( -31 \) |
$9.10511$ |
$(a^3+a^2-4a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.301614233$ |
$440.5254452$ |
2.003071688 |
\( -\frac{77286524488566078}{31} a^{3} + \frac{166085782662265724}{31} a^{2} + \frac{184093874850639127}{31} a - \frac{395610688650363197}{31} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 4\) , \( -a^{3} + a^{2} + 5 a - 4\) , \( a^{3} - 3 a\) , \( -116 a^{3} + 88 a^{2} + 840 a - 1067\) , \( 2720 a^{3} - 3047 a^{2} - 16831 a + 23245\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-4\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-4\right){x}^{2}+\left(-116a^{3}+88a^{2}+840a-1067\right){x}+2720a^{3}-3047a^{2}-16831a+23245$ |
| 31.2-c2 |
31.2-c |
$4$ |
$4$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( -31 \) |
$9.10511$ |
$(a^3+a^2-4a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.075403558$ |
$1762.101780$ |
2.003071688 |
\( \frac{155772}{31} a^{3} - \frac{267325}{31} a^{2} - \frac{634876}{31} a + \frac{1052962}{31} \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{2} + 4\) , \( a^{3} - 4 a\) , \( a^{3} - 3 a^{2} - 5 a + 12\) , \( 30 a^{3} + 64 a^{2} - 72 a - 153\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(a^{3}-3a^{2}-5a+12\right){x}+30a^{3}+64a^{2}-72a-153$ |
| 31.2-c3 |
31.2-c |
$4$ |
$4$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( 31^{4} \) |
$9.10511$ |
$(a^3+a^2-4a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.075403558$ |
$440.5254452$ |
2.003071688 |
\( \frac{59370852200354013489666}{923521} a^{3} - \frac{91630712350575600915204}{923521} a^{2} - \frac{274176613402283668981641}{923521} a + \frac{423153744048330031118195}{923521} \) |
\( \bigl[a^{3} - 4 a\) , \( -a^{3} + a^{2} + 5 a - 4\) , \( a^{3} + a^{2} - 4 a - 4\) , \( 80 a^{3} - 151 a^{2} - 203 a + 339\) , \( -712 a^{3} + 1513 a^{2} + 1703 a - 3582\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{3}+a^{2}-4a-4\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-4\right){x}^{2}+\left(80a^{3}-151a^{2}-203a+339\right){x}-712a^{3}+1513a^{2}+1703a-3582$ |
| 31.2-c4 |
31.2-c |
$4$ |
$4$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( 31^{2} \) |
$9.10511$ |
$(a^3+a^2-4a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.150807116$ |
$1762.101780$ |
2.003071688 |
\( \frac{77272583940}{961} a^{3} - \frac{109867494715}{961} a^{2} - \frac{391445107350}{961} a + \frac{581776625313}{961} \) |
\( \bigl[1\) , \( a^{2} - a - 3\) , \( a^{3} + a^{2} - 4 a - 4\) , \( 1477 a^{3} + 2281 a^{2} - 6825 a - 10537\) , \( 49010 a^{3} + 75642 a^{2} - 226327 a - 349309\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}+a^{2}-4a-4\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(1477a^{3}+2281a^{2}-6825a-10537\right){x}+49010a^{3}+75642a^{2}-226327a-349309$ |
| 31.2-d1 |
31.2-d |
$4$ |
$4$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( -31 \) |
$9.10511$ |
$(a^3+a^2-4a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1515.810669$ |
1.428231603 |
\( \frac{155772}{31} a^{3} - \frac{267325}{31} a^{2} - \frac{634876}{31} a + \frac{1052962}{31} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 4\) , \( 1\) , \( a\) , \( -2 a^{3} - 3 a^{2} + 9 a + 13\) , \( 6 a^{3} + 14 a^{2} - 12 a - 32\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-4\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-2a^{3}-3a^{2}+9a+13\right){x}+6a^{3}+14a^{2}-12a-32$ |
| 31.2-d2 |
31.2-d |
$4$ |
$4$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( 31^{4} \) |
$9.10511$ |
$(a^3+a^2-4a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$47.36908341$ |
1.428231603 |
\( \frac{59370852200354013489666}{923521} a^{3} - \frac{91630712350575600915204}{923521} a^{2} - \frac{274176613402283668981641}{923521} a + \frac{423153744048330031118195}{923521} \) |
\( \bigl[a^{2} - 4\) , \( a^{3} + a^{2} - 4 a - 3\) , \( a^{3} - 3 a + 1\) , \( 197 a^{3} - 416 a^{2} - 474 a + 985\) , \( -3002 a^{3} + 6453 a^{2} + 7149 a - 15377\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-3\right){x}^{2}+\left(197a^{3}-416a^{2}-474a+985\right){x}-3002a^{3}+6453a^{2}+7149a-15377$ |
| 31.2-d3 |
31.2-d |
$4$ |
$4$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( -31 \) |
$9.10511$ |
$(a^3+a^2-4a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$378.9526672$ |
1.428231603 |
\( -\frac{77286524488566078}{31} a^{3} + \frac{166085782662265724}{31} a^{2} + \frac{184093874850639127}{31} a - \frac{395610688650363197}{31} \) |
\( \bigl[a^{2} + a - 4\) , \( a^{3} + a^{2} - 4 a - 4\) , \( a^{2} - 4\) , \( 260 a^{3} - 624 a^{2} - 403 a + 1158\) , \( -9182 a^{3} + 19073 a^{2} + 24315 a - 49206\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-4\right){x}^{2}+\left(260a^{3}-624a^{2}-403a+1158\right){x}-9182a^{3}+19073a^{2}+24315a-49206$ |
| 31.2-d4 |
31.2-d |
$4$ |
$4$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( 31^{2} \) |
$9.10511$ |
$(a^3+a^2-4a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$757.9053345$ |
1.428231603 |
\( \frac{77272583940}{961} a^{3} - \frac{109867494715}{961} a^{2} - \frac{391445107350}{961} a + \frac{581776625313}{961} \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{3} + 3 a\) , \( a^{3} - 3 a + 1\) , \( 560 a^{3} + 866 a^{2} - 2597 a - 4013\) , \( -11564 a^{3} - 17840 a^{2} + 53415 a + 82420\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{3}+3a\right){x}^{2}+\left(560a^{3}+866a^{2}-2597a-4013\right){x}-11564a^{3}-17840a^{2}+53415a+82420$ |
| 31.2-e1 |
31.2-e |
$1$ |
$1$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( 31 \) |
$9.10511$ |
$(a^3+a^2-4a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.195376744$ |
$161.8086715$ |
1.906374917 |
\( -\frac{206255355828299}{31} a^{3} - \frac{318326661270219}{31} a^{2} + \frac{952494243687014}{31} a + \frac{1470043341319301}{31} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 3\) , \( -a^{3} - a^{2} + 4 a + 5\) , \( 1\) , \( 29 a^{3} - 62 a^{2} - 67 a + 150\) , \( 242 a^{3} - 518 a^{2} - 576 a + 1234\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-3\right){x}{y}+{y}={x}^{3}+\left(-a^{3}-a^{2}+4a+5\right){x}^{2}+\left(29a^{3}-62a^{2}-67a+150\right){x}+242a^{3}-518a^{2}-576a+1234$ |
| 31.2-f1 |
31.2-f |
$1$ |
$1$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( 31^{7} \) |
$9.10511$ |
$(a^3+a^2-4a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 7 \) |
$0.008173367$ |
$374.2505338$ |
1.291204819 |
\( -\frac{20658244006503}{27512614111} a^{3} + \frac{47471524533857}{27512614111} a^{2} + \frac{114350909406398}{27512614111} a - \frac{152350807490055}{27512614111} \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{3} - a^{2} + 3 a + 4\) , \( a^{3} - 3 a\) , \( a^{3} + 4 a^{2} - 9 a - 20\) , \( 5 a^{3} + 12 a^{2} - 25 a - 49\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{3}-a^{2}+3a+4\right){x}^{2}+\left(a^{3}+4a^{2}-9a-20\right){x}+5a^{3}+12a^{2}-25a-49$ |
| 49.1-a1 |
49.1-a |
$2$ |
$2$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{2} \) |
$9.64138$ |
$(-a^3-2a^2+5a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$722.3506244$ |
2.722461350 |
\( -\frac{37340}{7} a^{3} - \frac{44685}{7} a^{2} + \frac{165730}{7} a + \frac{224551}{7} \) |
\( \bigl[a + 1\) , \( a^{2} - a - 3\) , \( a^{3} + a^{2} - 3 a - 3\) , \( -a^{3} + 3 a + 1\) , \( a^{2} - 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-a^{3}+3a+1\right){x}+a^{2}-3$ |
| 49.1-a2 |
49.1-a |
$2$ |
$2$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{4} \) |
$9.64138$ |
$(-a^3-2a^2+5a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$361.1753122$ |
2.722461350 |
\( -\frac{7830569254}{49} a^{3} - \frac{11809522056}{49} a^{2} + 734527505 a + \frac{54902298079}{49} \) |
\( \bigl[a + 1\) , \( a^{2} - a - 3\) , \( a^{3} + a^{2} - 3 a - 3\) , \( -6 a^{3} - 5 a^{2} + 18 a + 6\) , \( 11 a^{2} + 6 a - 37\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-6a^{3}-5a^{2}+18a+6\right){x}+11a^{2}+6a-37$ |
| 49.1-b1 |
49.1-b |
$2$ |
$2$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{2} \) |
$9.64138$ |
$(-a^3-2a^2+5a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.037140192$ |
$2345.197526$ |
1.313098313 |
\( -\frac{37340}{7} a^{3} - \frac{44685}{7} a^{2} + \frac{165730}{7} a + \frac{224551}{7} \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{3} + a^{2} + 4 a - 4\) , \( a^{2} + a - 4\) , \( -a^{3} + a^{2} + 4 a - 5\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-4\right){x}^{2}+\left(-a^{3}+a^{2}+4a-5\right){x}$ |
| 49.1-b2 |
49.1-b |
$2$ |
$2$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{4} \) |
$9.64138$ |
$(-a^3-2a^2+5a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.018570096$ |
$2345.197526$ |
1.313098313 |
\( -\frac{7830569254}{49} a^{3} - \frac{11809522056}{49} a^{2} + 734527505 a + \frac{54902298079}{49} \) |
\( \bigl[a^{3} - 3 a + 1\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( a^{2} + a - 4\) , \( -10 a^{3} - 16 a^{2} + 24 a + 37\) , \( 14 a^{3} + 32 a^{2} - 34 a - 75\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-3\right){x}^{2}+\left(-10a^{3}-16a^{2}+24a+37\right){x}+14a^{3}+32a^{2}-34a-75$ |
| 49.2-a1 |
49.2-a |
$2$ |
$2$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{2} \) |
$9.64138$ |
$(a^3+a^2-4a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$722.3506244$ |
2.722461350 |
\( \frac{37340}{7} a^{3} - \frac{44685}{7} a^{2} - \frac{165730}{7} a + \frac{224551}{7} \) |
\( \bigl[a + 1\) , \( a^{2} - 3\) , \( a^{3} + a^{2} - 3 a - 3\) , \( -a^{3} + 3 a + 1\) , \( -a^{3} + a^{2} + 2 a - 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-a^{3}+3a+1\right){x}-a^{3}+a^{2}+2a-3$ |
| 49.2-a2 |
49.2-a |
$2$ |
$2$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{4} \) |
$9.64138$ |
$(a^3+a^2-4a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$361.1753122$ |
2.722461350 |
\( \frac{7830569254}{49} a^{3} - \frac{11809522056}{49} a^{2} - 734527505 a + \frac{54902298079}{49} \) |
\( \bigl[a + 1\) , \( a^{2} - 3\) , \( a^{3} + a^{2} - 3 a - 3\) , \( 4 a^{3} - 5 a^{2} - 12 a + 6\) , \( -a^{3} + 11 a^{2} - 4 a - 37\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(4a^{3}-5a^{2}-12a+6\right){x}-a^{3}+11a^{2}-4a-37$ |
| 49.2-b1 |
49.2-b |
$2$ |
$2$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{2} \) |
$9.64138$ |
$(a^3+a^2-4a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.037140192$ |
$2345.197526$ |
1.313098313 |
\( \frac{37340}{7} a^{3} - \frac{44685}{7} a^{2} - \frac{165730}{7} a + \frac{224551}{7} \) |
\( \bigl[a^{2} + a - 4\) , \( a^{2} - 4\) , \( a^{2} + a - 4\) , \( -a^{3} + a^{2} + 4 a - 5\) , \( -a^{3} + 4 a\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-a^{3}+a^{2}+4a-5\right){x}-a^{3}+4a$ |
| 49.2-b2 |
49.2-b |
$2$ |
$2$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{4} \) |
$9.64138$ |
$(a^3+a^2-4a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.018570096$ |
$2345.197526$ |
1.313098313 |
\( \frac{7830569254}{49} a^{3} - \frac{11809522056}{49} a^{2} - 734527505 a + \frac{54902298079}{49} \) |
\( \bigl[a^{3} - 3 a + 1\) , \( a^{2} - 3\) , \( a^{2} + a - 4\) , \( 10 a^{3} - 16 a^{2} - 26 a + 37\) , \( -15 a^{3} + 32 a^{2} + 38 a - 75\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(10a^{3}-16a^{2}-26a+37\right){x}-15a^{3}+32a^{2}+38a-75$ |
| 55.1-a1 |
55.1-a |
$2$ |
$2$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( - 5^{2} \cdot 11 \) |
$9.78161$ |
$(-a^3+a^2+4a-3), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.031090210$ |
$2846.489809$ |
2.668314086 |
\( -\frac{1422464}{55} a^{3} + \frac{309888}{5} a^{2} + \frac{3439616}{55} a - 146240 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 4\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( 1\) , \( 12 a^{3} + 25 a^{2} - 60 a - 107\) , \( -26 a^{3} - 35 a^{2} + 117 a + 168\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-4\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+a^{2}+3a-3\right){x}^{2}+\left(12a^{3}+25a^{2}-60a-107\right){x}-26a^{3}-35a^{2}+117a+168$ |
| 55.1-a2 |
55.1-a |
$2$ |
$2$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5 \cdot 11^{2} \) |
$9.78161$ |
$(-a^3+a^2+4a-3), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.062180420$ |
$1423.244904$ |
2.668314086 |
\( \frac{1734784}{55} a^{3} - \frac{2615424}{55} a^{2} - \frac{7957504}{55} a + \frac{12189504}{55} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{3} - a^{2} + 5 a + 3\) , \( a^{2} + a - 4\) , \( -3 a^{3} + 13 a - 1\) , \( a^{3} - 4 a^{2} - 5 a + 18\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{3}-a^{2}+5a+3\right){x}^{2}+\left(-3a^{3}+13a-1\right){x}+a^{3}-4a^{2}-5a+18$ |
| 55.1-b1 |
55.1-b |
$2$ |
$2$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5 \cdot 11^{2} \) |
$9.78161$ |
$(-a^3+a^2+4a-3), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.131364373$ |
$602.8326546$ |
2.387690469 |
\( \frac{1734784}{55} a^{3} - \frac{2615424}{55} a^{2} - \frac{7957504}{55} a + \frac{12189504}{55} \) |
\( \bigl[a^{3} - 4 a + 1\) , \( a^{3} + a^{2} - 3 a - 5\) , \( a^{3} + a^{2} - 3 a - 3\) , \( -a^{3} + a^{2} + 4 a - 3\) , \( -a^{3} + a^{2} + 3 a - 5\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-5\right){x}^{2}+\left(-a^{3}+a^{2}+4a-3\right){x}-a^{3}+a^{2}+3a-5$ |
| 55.1-b2 |
55.1-b |
$2$ |
$2$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( - 5^{2} \cdot 11 \) |
$9.78161$ |
$(-a^3+a^2+4a-3), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.065682186$ |
$1205.665309$ |
2.387690469 |
\( -\frac{1422464}{55} a^{3} + \frac{309888}{5} a^{2} + \frac{3439616}{55} a - 146240 \) |
\( \bigl[a^{3} - 4 a + 1\) , \( -a^{2} - a + 5\) , \( a^{2} + a - 4\) , \( 40 a^{3} + 52 a^{2} - 186 a - 241\) , \( 166 a^{3} + 251 a^{2} - 767 a - 1160\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}-a+5\right){x}^{2}+\left(40a^{3}+52a^{2}-186a-241\right){x}+166a^{3}+251a^{2}-767a-1160$ |
| 55.2-a1 |
55.2-a |
$2$ |
$2$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( 5 \cdot 11^{2} \) |
$9.78161$ |
$(a^3+2a^2-3a-5), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.062180420$ |
$1423.244904$ |
2.668314086 |
\( -\frac{1734784}{55} a^{3} - \frac{2615424}{55} a^{2} + \frac{7957504}{55} a + \frac{12189504}{55} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{2} + a + 3\) , \( a^{3} - 4 a\) , \( a^{3} + 2 a^{2} - 5 a - 6\) , \( a\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(a^{3}+2a^{2}-5a-6\right){x}+a$ |
| 55.2-a2 |
55.2-a |
$2$ |
$2$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( - 5^{2} \cdot 11 \) |
$9.78161$ |
$(a^3+2a^2-3a-5), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.031090210$ |
$2846.489809$ |
2.668314086 |
\( \frac{1422464}{55} a^{3} + \frac{309888}{5} a^{2} - \frac{3439616}{55} a - 146240 \) |
\( \bigl[a^{3} - 4 a + 1\) , \( a^{3} - 5 a - 1\) , \( a^{3} + a^{2} - 3 a - 3\) , \( -a^{3} - 4 a^{2} + 5 a + 11\) , \( -2 a^{3} + 3 a^{2} + 6 a - 13\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(a^{3}-5a-1\right){x}^{2}+\left(-a^{3}-4a^{2}+5a+11\right){x}-2a^{3}+3a^{2}+6a-13$ |
| 55.2-b1 |
55.2-b |
$2$ |
$2$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( 5 \cdot 11^{2} \) |
$9.78161$ |
$(a^3+2a^2-3a-5), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.131364373$ |
$602.8326546$ |
2.387690469 |
\( -\frac{1734784}{55} a^{3} - \frac{2615424}{55} a^{2} + \frac{7957504}{55} a + \frac{12189504}{55} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 4\) , \( a^{3} - 4 a\) , \( a^{3} + a^{2} - 3 a - 3\) , \( 4 a^{3} + 4 a^{2} - 18 a - 20\) , \( 5 a^{3} + 7 a^{2} - 23 a - 33\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-4\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+\left(4a^{3}+4a^{2}-18a-20\right){x}+5a^{3}+7a^{2}-23a-33$ |
| 55.2-b2 |
55.2-b |
$2$ |
$2$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( - 5^{2} \cdot 11 \) |
$9.78161$ |
$(a^3+2a^2-3a-5), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.065682186$ |
$1205.665309$ |
2.387690469 |
\( \frac{1422464}{55} a^{3} + \frac{309888}{5} a^{2} - \frac{3439616}{55} a - 146240 \) |
\( \bigl[a^{2} + a - 3\) , \( a + 1\) , \( a^{2} + a - 4\) , \( -5 a^{3} + 10 a^{2} + 26 a - 43\) , \( -9 a^{3} + 17 a^{2} + 43 a - 73\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-5a^{3}+10a^{2}+26a-43\right){x}-9a^{3}+17a^{2}+43a-73$ |
| 64.1-a1 |
64.1-a |
$4$ |
$4$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( - 2^{16} \) |
$9.96867$ |
$(-a^3+4a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$404.3250407$ |
1.523857333 |
\( -423804859826500 a^{3} + 910740175453692 a^{2} + 1009488771499464 a - 2169352142992340 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 4\) , \( a^{3} + a^{2} - 3 a - 4\) , \( a^{3} - 4 a + 1\) , \( 28 a^{3} + 57 a^{2} - 82 a - 162\) , \( 10 a^{3} + 15 a^{2} - 47 a - 71\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-4\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-4\right){x}^{2}+\left(28a^{3}+57a^{2}-82a-162\right){x}+10a^{3}+15a^{2}-47a-71$ |
| 64.1-a2 |
64.1-a |
$4$ |
$4$ |
4.4.4400.1 |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( - 2^{16} \) |
$9.96867$ |
$(-a^3+4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$101.0812601$ |
1.523857333 |
\( -3620711054524 a^{3} - 5588069320444 a^{2} + 16720566728760 a + 25805894079396 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 4\) , \( a^{3} - a^{2} - 3 a + 3\) , \( a^{3} - 4 a + 1\) , \( 12 a^{3} - 28 a^{2} - 21 a + 53\) , \( -111 a^{3} + 232 a^{2} + 288 a - 590\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-4\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+3\right){x}^{2}+\left(12a^{3}-28a^{2}-21a+53\right){x}-111a^{3}+232a^{2}+288a-590$ |
*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.
