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 |
7.1-a1 |
7.1-a |
$6$ |
$8$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{2} \) |
$4.76909$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$256$ |
\( 2 \) |
$1$ |
$0.551754621$ |
1.830242350 |
\( -\frac{28836360033558018913}{49} a^{2} + \frac{52590469545304245043}{49} a + \frac{245041987087172175919}{49} \) |
\( \bigl[a^{2} - a - 5\) , \( a\) , \( a^{2} - 2 a - 6\) , \( 163 a^{2} - 413 a - 1721\) , \( 2375 a^{2} - 6606 a - 25325\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-2a-6\right){y}={x}^{3}+a{x}^{2}+\left(163a^{2}-413a-1721\right){x}+2375a^{2}-6606a-25325$ |
7.1-a2 |
7.1-a |
$6$ |
$8$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
7.1 |
\( 7 \) |
\( 7^{4} \) |
$4.76909$ |
$(a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$64$ |
\( 2^{2} \) |
$1$ |
$4.414036972$ |
1.830242350 |
\( \frac{3159692805341440}{2401} a^{2} - \frac{9930285721910369}{2401} a - \frac{10319572364155346}{2401} \) |
\( \bigl[a^{2} - a - 5\) , \( a\) , \( a^{2} - 2 a - 6\) , \( 3 a^{2} + 12 a - 76\) , \( 9 a^{2} - 21 a - 356\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-2a-6\right){y}={x}^{3}+a{x}^{2}+\left(3a^{2}+12a-76\right){x}+9a^{2}-21a-356$ |
7.1-a3 |
7.1-a |
$6$ |
$8$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{16} \) |
$4.76909$ |
$(a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$17.65614788$ |
1.830242350 |
\( \frac{63155835815034624}{33232930569601} a^{2} + \frac{279346093826179201}{33232930569601} a + \frac{269938185007911394}{33232930569601} \) |
\( \bigl[a^{2} - a - 5\) , \( a\) , \( a^{2} - 2 a - 6\) , \( 3 a^{2} + 2 a - 16\) , \( a^{2} + 5 a\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-2a-6\right){y}={x}^{3}+a{x}^{2}+\left(3a^{2}+2a-16\right){x}+a^{2}+5a$ |
7.1-a4 |
7.1-a |
$6$ |
$8$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
7.1 |
\( 7 \) |
\( 7^{8} \) |
$4.76909$ |
$(a)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{3} \) |
$1$ |
$35.31229577$ |
1.830242350 |
\( \frac{2290456590017}{5764801} a^{2} - \frac{7248961638668}{5764801} a - \frac{7268162845212}{5764801} \) |
\( \bigl[a^{2} - a - 5\) , \( a\) , \( a^{2} - 2 a - 6\) , \( 3 a^{2} + 7 a - 6\) , \( 5 a^{2} + 10 a - 6\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-2a-6\right){y}={x}^{3}+a{x}^{2}+\left(3a^{2}+7a-6\right){x}+5a^{2}+10a-6$ |
7.1-a5 |
7.1-a |
$6$ |
$8$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
7.1 |
\( 7 \) |
\( 7^{4} \) |
$4.76909$ |
$(a)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$70.62459155$ |
1.830242350 |
\( \frac{909723}{2401} a^{2} - \frac{2152223}{2401} a - \frac{2389809}{2401} \) |
\( \bigl[a^{2} - a - 5\) , \( a\) , \( a^{2} - 2 a - 6\) , \( 3 a^{2} + 7 a - 1\) , \( 5 a^{2} + 14 a + 5\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-2a-6\right){y}={x}^{3}+a{x}^{2}+\left(3a^{2}+7a-1\right){x}+5a^{2}+14a+5$ |
7.1-a6 |
7.1-a |
$6$ |
$8$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$4.76909$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$256$ |
\( 2 \) |
$1$ |
$0.551754621$ |
1.830242350 |
\( \frac{683934083230577981724699489}{49} a^{2} - \frac{2149259682136725506683278131}{49} a - \frac{2234561938913398699756399455}{49} \) |
\( \bigl[a^{2} - a - 5\) , \( a\) , \( a^{2} - 2 a - 6\) , \( -157 a^{2} + 517 a + 449\) , \( -2321 a^{2} + 7300 a + 7253\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-2a-6\right){y}={x}^{3}+a{x}^{2}+\left(-157a^{2}+517a+449\right){x}-2321a^{2}+7300a+7253$ |
7.1-b1 |
7.1-b |
$6$ |
$8$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
7.1 |
\( 7 \) |
\( 7^{4} \) |
$4.76909$ |
$(a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.094200040$ |
$135.2393424$ |
2.752359336 |
\( \frac{909723}{2401} a^{2} - \frac{2152223}{2401} a - \frac{2389809}{2401} \) |
\( \bigl[1\) , \( -a^{2} + 3 a + 7\) , \( a^{2} - a - 5\) , \( -3 a^{2} + 8 a + 16\) , \( -2 a - 2\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(-a^{2}+3a+7\right){x}^{2}+\left(-3a^{2}+8a+16\right){x}-2a-2$ |
7.1-b2 |
7.1-b |
$6$ |
$8$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{16} \) |
$4.76909$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$8.376800161$ |
$8.452458901$ |
2.752359336 |
\( \frac{63155835815034624}{33232930569601} a^{2} + \frac{279346093826179201}{33232930569601} a + \frac{269938185007911394}{33232930569601} \) |
\( \bigl[1\) , \( -a^{2} + 3 a + 7\) , \( a^{2} - a - 5\) , \( -28 a^{2} + 88 a + 91\) , \( -225 a^{2} + 708 a + 720\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(-a^{2}+3a+7\right){x}^{2}+\left(-28a^{2}+88a+91\right){x}-225a^{2}+708a+720$ |
7.1-b3 |
7.1-b |
$6$ |
$8$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
7.1 |
\( 7 \) |
\( 7^{8} \) |
$4.76909$ |
$(a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$4.188400080$ |
$67.61967121$ |
2.752359336 |
\( \frac{2290456590017}{5764801} a^{2} - \frac{7248961638668}{5764801} a - \frac{7268162845212}{5764801} \) |
\( \bigl[1\) , \( -a^{2} + 3 a + 7\) , \( a^{2} - a - 5\) , \( -33 a^{2} + 103 a + 111\) , \( -165 a^{2} + 517 a + 535\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(-a^{2}+3a+7\right){x}^{2}+\left(-33a^{2}+103a+111\right){x}-165a^{2}+517a+535$ |
7.1-b4 |
7.1-b |
$6$ |
$8$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{2} \) |
$4.76909$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$4.188400080$ |
$16.90491780$ |
2.752359336 |
\( -\frac{28836360033558018913}{49} a^{2} + \frac{52590469545304245043}{49} a + \frac{245041987087172175919}{49} \) |
\( \bigl[1\) , \( -a^{2} + 3 a + 7\) , \( a^{2} - a - 5\) , \( -383 a^{2} + 1388 a + 496\) , \( -14020 a^{2} + 42098 a + 53588\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(-a^{2}+3a+7\right){x}^{2}+\left(-383a^{2}+1388a+496\right){x}-14020a^{2}+42098a+53588$ |
7.1-b5 |
7.1-b |
$6$ |
$8$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
7.1 |
\( 7 \) |
\( 7^{4} \) |
$4.76909$ |
$(a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$8.376800161$ |
$33.80983560$ |
2.752359336 |
\( \frac{3159692805341440}{2401} a^{2} - \frac{9930285721910369}{2401} a - \frac{10319572364155346}{2401} \) |
\( \bigl[1\) , \( -a^{2} + 3 a + 7\) , \( a^{2} - a - 5\) , \( -518 a^{2} + 1638 a + 1651\) , \( -12545 a^{2} + 39402 a + 41058\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(-a^{2}+3a+7\right){x}^{2}+\left(-518a^{2}+1638a+1651\right){x}-12545a^{2}+39402a+41058$ |
7.1-b6 |
7.1-b |
$6$ |
$8$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$4.76909$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$16.75360032$ |
$4.226229450$ |
2.752359336 |
\( \frac{683934083230577981724699489}{49} a^{2} - \frac{2149259682136725506683278131}{49} a - \frac{2234561938913398699756399455}{49} \) |
\( \bigl[1\) , \( -a^{2} + 3 a + 7\) , \( a^{2} - a - 5\) , \( -8413 a^{2} + 26448 a + 27446\) , \( -833690 a^{2} + 2619846 a + 2723920\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(-a^{2}+3a+7\right){x}^{2}+\left(-8413a^{2}+26448a+27446\right){x}-833690a^{2}+2619846a+2723920$ |
8.1-a1 |
8.1-a |
$2$ |
$3$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{9} \) |
$4.87642$ |
$(2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$2.356809401$ |
$146.4904636$ |
2.982395338 |
\( -\frac{27353}{8} a^{2} + \frac{105205}{8} a - \frac{1545}{4} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a^{2} - a - 5\) , \( -a^{2} + 8 a - 5\) , \( 8 a^{2} - 27 a - 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a^{2}+8a-5\right){x}+8a^{2}-27a-2$ |
8.1-a2 |
8.1-a |
$2$ |
$3$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{27} \) |
$4.87642$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$7.070428204$ |
$5.425572728$ |
2.982395338 |
\( -\frac{339837761601}{512} a^{2} - \frac{1008043721045}{512} a - \frac{599775655369}{512} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a^{2} - a - 5\) , \( 4 a^{2} - 27 a + 55\) , \( 27 a^{2} - 74 a - 115\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(4a^{2}-27a+55\right){x}+27a^{2}-74a-115$ |
8.1-b1 |
8.1-b |
$2$ |
$3$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{9} \) |
$4.87642$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.286960720$ |
$120.9265947$ |
2.697852387 |
\( -\frac{27353}{8} a^{2} + \frac{105205}{8} a - \frac{1545}{4} \) |
\( \bigl[a^{2} - 2 a - 6\) , \( a^{2} - 2 a - 7\) , \( a\) , \( 4 a^{2} - 9 a - 30\) , \( 4 a^{2} - 8 a - 35\bigr] \) |
${y}^2+\left(a^{2}-2a-6\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-2a-7\right){x}^{2}+\left(4a^{2}-9a-30\right){x}+4a^{2}-8a-35$ |
8.1-b2 |
8.1-b |
$2$ |
$3$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{27} \) |
$4.87642$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.860882161$ |
$40.30886492$ |
2.697852387 |
\( -\frac{339837761601}{512} a^{2} - \frac{1008043721045}{512} a - \frac{599775655369}{512} \) |
\( \bigl[a^{2} - 2 a - 6\) , \( a^{2} - 2 a - 7\) , \( a\) , \( -16 a^{2} + 26 a + 140\) , \( 12 a^{2} - 23 a - 99\bigr] \) |
${y}^2+\left(a^{2}-2a-6\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-2a-7\right){x}^{2}+\left(-16a^{2}+26a+140\right){x}+12a^{2}-23a-99$ |
13.1-a1 |
13.1-a |
$2$ |
$2$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
13.1 |
\( 13 \) |
\( 13^{2} \) |
$5.28741$ |
$(a^2-3a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.798508442$ |
$113.7406028$ |
3.530522212 |
\( \frac{1940676136}{169} a^{2} - \frac{3539834321}{169} a - \frac{16489182614}{169} \) |
\( \bigl[a + 1\) , \( -a^{2} + 3 a + 5\) , \( a + 1\) , \( -a^{2} + 4 a + 5\) , \( a + 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+3a+5\right){x}^{2}+\left(-a^{2}+4a+5\right){x}+a+1$ |
13.1-a2 |
13.1-a |
$2$ |
$2$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
13.1 |
\( 13 \) |
\( 13 \) |
$5.28741$ |
$(a^2-3a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.597016884$ |
$113.7406028$ |
3.530522212 |
\( -\frac{10824428774162257}{13} a^{2} + \frac{19741105456676281}{13} a + \frac{91982454588646569}{13} \) |
\( \bigl[a + 1\) , \( -a^{2} + 3 a + 5\) , \( a + 1\) , \( -6 a^{2} + 14 a + 15\) , \( 21 a^{2} - 92 a - 90\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+3a+5\right){x}^{2}+\left(-6a^{2}+14a+15\right){x}+21a^{2}-92a-90$ |
13.1-b1 |
13.1-b |
$2$ |
$7$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
13.1 |
\( 13 \) |
\( 13 \) |
$5.28741$ |
$(a^2-3a-5)$ |
$1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 1 \) |
$6.086570486$ |
$299.9195632$ |
2.896378243 |
\( \frac{5287458}{13} a^{2} - \frac{9665008}{13} a - \frac{44823817}{13} \) |
\( \bigl[a^{2} - 2 a - 5\) , \( a^{2} - 3 a - 5\) , \( a^{2} - a - 5\) , \( 3 a^{2} - 10 a - 15\) , \( 2 a^{2} - 8 a - 11\bigr] \) |
${y}^2+\left(a^{2}-2a-5\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a^{2}-3a-5\right){x}^{2}+\left(3a^{2}-10a-15\right){x}+2a^{2}-8a-11$ |
13.1-b2 |
13.1-b |
$2$ |
$7$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
13.1 |
\( 13 \) |
\( 13^{7} \) |
$5.28741$ |
$(a^2-3a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.3 |
$1$ |
\( 1 \) |
$42.60599340$ |
$0.874401058$ |
2.896378243 |
\( \frac{59458245109305170602}{62748517} a^{2} - \frac{187197696596990380780}{62748517} a - \frac{194551739766325064917}{62748517} \) |
\( \bigl[a^{2} - 2 a - 5\) , \( a^{2} - 3 a - 5\) , \( a^{2} - a - 5\) , \( -527 a^{2} + 1465 a + 1560\) , \( -14200 a^{2} + 42364 a + 44530\bigr] \) |
${y}^2+\left(a^{2}-2a-5\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a^{2}-3a-5\right){x}^{2}+\left(-527a^{2}+1465a+1560\right){x}-14200a^{2}+42364a+44530$ |
13.1-c1 |
13.1-c |
$2$ |
$7$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
13.1 |
\( 13 \) |
\( 13^{7} \) |
$5.28741$ |
$(a^2-3a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.3 |
$1$ |
\( 1 \) |
$3.684300274$ |
$9.959558664$ |
2.852784842 |
\( \frac{59458245109305170602}{62748517} a^{2} - \frac{187197696596990380780}{62748517} a - \frac{194551739766325064917}{62748517} \) |
\( \bigl[1\) , \( -a - 1\) , \( a^{2} - 2 a - 6\) , \( -1118 a^{2} - 3252 a - 1918\) , \( 78452 a^{2} + 232952 a + 138657\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2a-6\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1118a^{2}-3252a-1918\right){x}+78452a^{2}+232952a+138657$ |
13.1-c2 |
13.1-c |
$2$ |
$7$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
13.1 |
\( 13 \) |
\( 13 \) |
$5.28741$ |
$(a^2-3a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.1 |
$1$ |
\( 1 \) |
$0.526328610$ |
$69.71691065$ |
2.852784842 |
\( \frac{5287458}{13} a^{2} - \frac{9665008}{13} a - \frac{44823817}{13} \) |
\( \bigl[1\) , \( -a - 1\) , \( a^{2} - 2 a - 6\) , \( 2 a^{2} + 8 a + 7\) , \( -a^{2} - 4 a - 6\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2a-6\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a^{2}+8a+7\right){x}-a^{2}-4a-6$ |
13.1-d1 |
13.1-d |
$2$ |
$2$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
13.1 |
\( 13 \) |
\( 13 \) |
$5.28741$ |
$(a^2-3a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$4.559800508$ |
$36.07630523$ |
3.197288384 |
\( -\frac{10824428774162257}{13} a^{2} + \frac{19741105456676281}{13} a + \frac{91982454588646569}{13} \) |
\( \bigl[a^{2} - 2 a - 6\) , \( -a^{2} + a + 6\) , \( 1\) , \( -39 a^{2} - 99 a - 35\) , \( 500 a^{2} + 1491 a + 899\bigr] \) |
${y}^2+\left(a^{2}-2a-6\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(-39a^{2}-99a-35\right){x}+500a^{2}+1491a+899$ |
13.1-d2 |
13.1-d |
$2$ |
$2$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
13.1 |
\( 13 \) |
\( 13^{2} \) |
$5.28741$ |
$(a^2-3a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.279900254$ |
$36.07630523$ |
3.197288384 |
\( \frac{1940676136}{169} a^{2} - \frac{3539834321}{169} a - \frac{16489182614}{169} \) |
\( \bigl[a^{2} - 2 a - 6\) , \( -a^{2} + a + 6\) , \( 1\) , \( -4 a^{2} + 6 a + 30\) , \( 15 a^{2} + 58 a + 55\bigr] \) |
${y}^2+\left(a^{2}-2a-6\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(-4a^{2}+6a+30\right){x}+15a^{2}+58a+55$ |
19.2-a1 |
19.2-a |
$4$ |
$6$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
19.2 |
\( 19 \) |
\( 19^{2} \) |
$5.63263$ |
$(-2a-3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2 \) |
$1$ |
$272.9251678$ |
1.571750920 |
\( \frac{10351613}{361} a^{2} - \frac{19233431}{361} a - \frac{86973528}{361} \) |
\( \bigl[a^{2} - a - 5\) , \( a^{2} - 2 a - 7\) , \( a^{2} - 2 a - 6\) , \( 2 a^{2} + 4 a - 4\) , \( 2 a^{2} + 8 a + 2\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-2a-6\right){y}={x}^{3}+\left(a^{2}-2a-7\right){x}^{2}+\left(2a^{2}+4a-4\right){x}+2a^{2}+8a+2$ |
19.2-a2 |
19.2-a |
$4$ |
$6$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
19.2 |
\( 19 \) |
\( 19 \) |
$5.63263$ |
$(-2a-3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$16$ |
\( 1 \) |
$1$ |
$136.4625839$ |
1.571750920 |
\( -\frac{95603982335}{19} a^{2} + \frac{174317043700}{19} a + \frac{812635732213}{19} \) |
\( \bigl[a^{2} - a - 5\) , \( a^{2} - 2 a - 7\) , \( a^{2} - 2 a - 6\) , \( -3 a^{2} + 19 a + 6\) , \( -21 a^{2} + 73 a + 80\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-2a-6\right){y}={x}^{3}+\left(a^{2}-2a-7\right){x}^{2}+\left(-3a^{2}+19a+6\right){x}-21a^{2}+73a+80$ |
19.2-a3 |
19.2-a |
$4$ |
$6$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
19.2 |
\( 19 \) |
\( 19^{6} \) |
$5.63263$ |
$(-2a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$10.10833954$ |
1.571750920 |
\( \frac{389738496302844913}{47045881} a^{2} - \frac{1224751414621660754}{47045881} a - \frac{1273360707204279647}{47045881} \) |
\( \bigl[a^{2} - a - 5\) , \( a^{2} - 2 a - 7\) , \( a^{2} - 2 a - 6\) , \( -28 a^{2} + 99 a + 96\) , \( -206 a^{2} + 665 a + 684\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-2a-6\right){y}={x}^{3}+\left(a^{2}-2a-7\right){x}^{2}+\left(-28a^{2}+99a+96\right){x}-206a^{2}+665a+684$ |
19.2-a4 |
19.2-a |
$4$ |
$6$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
19.2 |
\( 19 \) |
\( 19^{3} \) |
$5.63263$ |
$(-2a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$16$ |
\( 3 \) |
$1$ |
$5.054169774$ |
1.571750920 |
\( \frac{3792063147582937304898720}{6859} a^{2} - \frac{11916540840776906741774375}{6859} a - \frac{12389498033962182988047897}{6859} \) |
\( \bigl[a^{2} - a - 5\) , \( a^{2} - 2 a - 7\) , \( a^{2} - 2 a - 6\) , \( -483 a^{2} + 1524 a + 1571\) , \( -12115 a^{2} + 38054 a + 39573\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-2a-6\right){y}={x}^{3}+\left(a^{2}-2a-7\right){x}^{2}+\left(-483a^{2}+1524a+1571\right){x}-12115a^{2}+38054a+39573$ |
19.2-b1 |
19.2-b |
$4$ |
$6$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
19.2 |
\( 19 \) |
\( 19^{3} \) |
$5.63263$ |
$(-2a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$16$ |
\( 3 \) |
$1$ |
$4.956675476$ |
1.541432043 |
\( \frac{3792063147582937304898720}{6859} a^{2} - \frac{11916540840776906741774375}{6859} a - \frac{12389498033962182988047897}{6859} \) |
\( \bigl[a\) , \( -a + 1\) , \( a^{2} - a - 6\) , \( -40 a^{2} - 71 a - 41\) , \( 216 a^{2} + 917 a + 590\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-40a^{2}-71a-41\right){x}+216a^{2}+917a+590$ |
19.2-b2 |
19.2-b |
$4$ |
$6$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
19.2 |
\( 19 \) |
\( 19 \) |
$5.63263$ |
$(-2a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$16$ |
\( 1 \) |
$1$ |
$14.87002642$ |
1.541432043 |
\( -\frac{95603982335}{19} a^{2} + \frac{174317043700}{19} a + \frac{812635732213}{19} \) |
\( \bigl[a\) , \( -a + 1\) , \( a^{2} - a - 6\) , \( -10 a^{2} - 41 a - 36\) , \( -85 a^{2} - 268 a - 183\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-10a^{2}-41a-36\right){x}-85a^{2}-268a-183$ |
19.2-b3 |
19.2-b |
$4$ |
$6$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
19.2 |
\( 19 \) |
\( 19^{2} \) |
$5.63263$ |
$(-2a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$29.74005285$ |
1.541432043 |
\( \frac{10351613}{361} a^{2} - \frac{19233431}{361} a - \frac{86973528}{361} \) |
\( \bigl[a\) , \( -a + 1\) , \( a^{2} - a - 6\) , \( -6 a - 6\) , \( -a^{2} - 9 a - 12\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6a-6\right){x}-a^{2}-9a-12$ |
19.2-b4 |
19.2-b |
$4$ |
$6$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
19.2 |
\( 19 \) |
\( 19^{6} \) |
$5.63263$ |
$(-2a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$9.913350952$ |
1.541432043 |
\( \frac{389738496302844913}{47045881} a^{2} - \frac{1224751414621660754}{47045881} a - \frac{1273360707204279647}{47045881} \) |
\( \bigl[a\) , \( -a + 1\) , \( a^{2} - a - 6\) , \( 5 a^{2} + 14 a + 9\) , \( 29 a^{2} + 89 a + 49\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(5a^{2}+14a+9\right){x}+29a^{2}+89a+49$ |
19.3-a1 |
19.3-a |
$2$ |
$3$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
19.3 |
\( 19 \) |
\( 19^{3} \) |
$5.63263$ |
$(a-3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$9$ |
\( 3 \) |
$1$ |
$35.62197492$ |
2.769439609 |
\( -\frac{5575931}{6859} a^{2} + \frac{11039397}{6859} a + \frac{24746668}{6859} \) |
\( \bigl[a\) , \( -a^{2} + a + 6\) , \( a^{2} - 2 a - 6\) , \( -3 a^{2} + 8 a + 13\) , \( -6 a^{2} + 19 a + 18\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-2a-6\right){y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(-3a^{2}+8a+13\right){x}-6a^{2}+19a+18$ |
19.3-a2 |
19.3-a |
$2$ |
$3$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
19.3 |
\( 19 \) |
\( 19 \) |
$5.63263$ |
$(a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$81$ |
\( 1 \) |
$1$ |
$1.319332404$ |
2.769439609 |
\( -\frac{211654900994}{19} a^{2} + \frac{496556189253}{19} a + \frac{555084352101}{19} \) |
\( \bigl[a\) , \( -a^{2} + a + 6\) , \( a^{2} - 2 a - 6\) , \( -213 a^{2} + 683 a + 638\) , \( -3641 a^{2} + 11518 a + 11593\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-2a-6\right){y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(-213a^{2}+683a+638\right){x}-3641a^{2}+11518a+11593$ |
19.3-b1 |
19.3-b |
$2$ |
$3$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
19.3 |
\( 19 \) |
\( - 19^{9} \) |
$5.63263$ |
$(a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 3^{2} \) |
$1$ |
$8.477371439$ |
1.977226274 |
\( -\frac{17515413843775488}{322687697779} a^{2} + \frac{27478062794358784}{322687697779} a + \frac{166506431699075072}{322687697779} \) |
\( \bigl[0\) , \( 1\) , \( a^{2} - a - 6\) , \( -9 a^{2} - 27 a - 18\) , \( -210 a^{2} - 627 a - 381\bigr] \) |
${y}^2+\left(a^{2}-a-6\right){y}={x}^{3}+{x}^{2}+\left(-9a^{2}-27a-18\right){x}-210a^{2}-627a-381$ |
19.3-b2 |
19.3-b |
$2$ |
$3$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
19.3 |
\( 19 \) |
\( - 19^{3} \) |
$5.63263$ |
$(a-3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$228.8890288$ |
1.977226274 |
\( \frac{18829312}{6859} a^{2} - \frac{73785344}{6859} a - \frac{2629632}{6859} \) |
\( \bigl[0\) , \( 1\) , \( a^{2} - a - 6\) , \( a^{2} + 3 a + 2\) , \( 8 a^{2} + 20 a + 6\bigr] \) |
${y}^2+\left(a^{2}-a-6\right){y}={x}^{3}+{x}^{2}+\left(a^{2}+3a+2\right){x}+8a^{2}+20a+6$ |
19.3-c1 |
19.3-c |
$2$ |
$3$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
19.3 |
\( 19 \) |
\( 19 \) |
$5.63263$ |
$(a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1.557121048$ |
$30.52325118$ |
3.695107449 |
\( -\frac{211654900994}{19} a^{2} + \frac{496556189253}{19} a + \frac{555084352101}{19} \) |
\( \bigl[a + 1\) , \( a^{2} - a - 7\) , \( 1\) , \( 10 a^{2} - 14 a - 112\) , \( -104 a^{2} + 204 a + 828\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-7\right){x}^{2}+\left(10a^{2}-14a-112\right){x}-104a^{2}+204a+828$ |
19.3-c2 |
19.3-c |
$2$ |
$3$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
19.3 |
\( 19 \) |
\( 19^{3} \) |
$5.63263$ |
$(a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.519040349$ |
$91.56975355$ |
3.695107449 |
\( -\frac{5575931}{6859} a^{2} + \frac{11039397}{6859} a + \frac{24746668}{6859} \) |
\( \bigl[a + 1\) , \( a^{2} - a - 7\) , \( 1\) , \( 6 a + 13\) , \( 2 a^{2} + 4 a - 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-7\right){x}^{2}+\left(6a+13\right){x}+2a^{2}+4a-1$ |
19.3-d1 |
19.3-d |
$2$ |
$3$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
19.3 |
\( 19 \) |
\( - 19^{3} \) |
$5.63263$ |
$(a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.404182320$ |
$107.1047586$ |
3.365580522 |
\( \frac{18829312}{6859} a^{2} - \frac{73785344}{6859} a - \frac{2629632}{6859} \) |
\( \bigl[0\) , \( a^{2} - 3 a - 7\) , \( a\) , \( -a^{2} + 3 a + 8\) , \( -a - 3\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a^{2}-3a-7\right){x}^{2}+\left(-a^{2}+3a+8\right){x}-a-3$ |
19.3-d2 |
19.3-d |
$2$ |
$3$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
19.3 |
\( 19 \) |
\( - 19^{9} \) |
$5.63263$ |
$(a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1.212546961$ |
$35.70158622$ |
3.365580522 |
\( -\frac{17515413843775488}{322687697779} a^{2} + \frac{27478062794358784}{322687697779} a + \frac{166506431699075072}{322687697779} \) |
\( \bigl[0\) , \( a^{2} - 3 a - 7\) , \( a\) , \( -11 a^{2} + 33 a + 38\) , \( -53 a^{2} + 173 a + 179\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a^{2}-3a-7\right){x}^{2}+\left(-11a^{2}+33a+38\right){x}-53a^{2}+173a+179$ |
31.2-a1 |
31.2-a |
$1$ |
$1$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
31.2 |
\( 31 \) |
\( -31 \) |
$6.11148$ |
$(a^2-a-8)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$108.7500513$ |
2.818266912 |
\( -\frac{286913}{31} a^{2} + \frac{392000}{31} a + \frac{2705355}{31} \) |
\( \bigl[a^{2} - 2 a - 6\) , \( -a^{2} + a + 7\) , \( a^{2} - a - 5\) , \( -5 a^{2} + a + 24\) , \( -7 a^{2} - 3 a + 25\bigr] \) |
${y}^2+\left(a^{2}-2a-6\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(-a^{2}+a+7\right){x}^{2}+\left(-5a^{2}+a+24\right){x}-7a^{2}-3a+25$ |
31.2-b1 |
31.2-b |
$1$ |
$1$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
31.2 |
\( 31 \) |
\( -31 \) |
$6.11148$ |
$(a^2-a-8)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.287522651$ |
$177.3186803$ |
3.963697117 |
\( -\frac{286913}{31} a^{2} + \frac{392000}{31} a + \frac{2705355}{31} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -2 a^{2} + 9 a + 9\) , \( -5 a^{2} + 18 a + 18\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-2a^{2}+9a+9\right){x}-5a^{2}+18a+18$ |
49.2-a1 |
49.2-a |
$6$ |
$8$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
49.2 |
\( 7^{2} \) |
\( - 7^{8} \) |
$6.59607$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$64$ |
\( 2^{2} \) |
$1$ |
$1.419221852$ |
2.353872389 |
\( -\frac{28836360033558018913}{49} a^{2} + \frac{52590469545304245043}{49} a + \frac{245041987087172175919}{49} \) |
\( \bigl[a^{2} - 2 a - 6\) , \( -a^{2} + 2 a + 5\) , \( a + 1\) , \( 4318 a^{2} - 7917 a - 37083\) , \( -271625 a^{2} + 494918 a + 2305350\bigr] \) |
${y}^2+\left(a^{2}-2a-6\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}+\left(4318a^{2}-7917a-37083\right){x}-271625a^{2}+494918a+2305350$ |
49.2-a2 |
49.2-a |
$6$ |
$8$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{10} \) |
$6.59607$ |
$(a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$64$ |
\( 2^{2} \) |
$1$ |
$5.676887411$ |
2.353872389 |
\( \frac{3159692805341440}{2401} a^{2} - \frac{9930285721910369}{2401} a - \frac{10319572364155346}{2401} \) |
\( \bigl[a^{2} - 2 a - 6\) , \( -a^{2} + 2 a + 5\) , \( a + 1\) , \( 233 a^{2} - 382 a - 2188\) , \( -4057 a^{2} + 7691 a + 33255\bigr] \) |
${y}^2+\left(a^{2}-2a-6\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}+\left(233a^{2}-382a-2188\right){x}-4057a^{2}+7691a+33255$ |
49.2-a3 |
49.2-a |
$6$ |
$8$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{8} \) |
$6.59607$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$256$ |
\( 2 \) |
$1$ |
$0.709610926$ |
2.353872389 |
\( \frac{683934083230577981724699489}{49} a^{2} - \frac{2149259682136725506683278131}{49} a - \frac{2234561938913398699756399455}{49} \) |
\( \bigl[a^{2} - 2 a - 6\) , \( -a^{2} + 2 a + 5\) , \( a + 1\) , \( -332 a^{2} + 1393 a - 333\) , \( -19629 a^{2} + 56548 a + 84404\bigr] \) |
${y}^2+\left(a^{2}-2a-6\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}+\left(-332a^{2}+1393a-333\right){x}-19629a^{2}+56548a+84404$ |
49.2-a4 |
49.2-a |
$6$ |
$8$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
49.2 |
\( 7^{2} \) |
\( - 7^{22} \) |
$6.59607$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$5.676887411$ |
2.353872389 |
\( \frac{63155835815034624}{33232930569601} a^{2} + \frac{279346093826179201}{33232930569601} a + \frac{269938185007911394}{33232930569601} \) |
\( \bigl[a^{2} - 2 a - 6\) , \( -a^{2} + 2 a + 5\) , \( a + 1\) , \( 33 a^{2} - 62 a - 298\) , \( 195 a^{2} - 343 a - 1661\bigr] \) |
${y}^2+\left(a^{2}-2a-6\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}+\left(33a^{2}-62a-298\right){x}+195a^{2}-343a-1661$ |
49.2-a5 |
49.2-a |
$6$ |
$8$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{14} \) |
$6.59607$ |
$(a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$16$ |
\( 2^{2} \) |
$1$ |
$22.70754964$ |
2.353872389 |
\( \frac{2290456590017}{5764801} a^{2} - \frac{7248961638668}{5764801} a - \frac{7268162845212}{5764801} \) |
\( \bigl[a^{2} - 2 a - 6\) , \( -a^{2} + 2 a + 5\) , \( a + 1\) , \( 13 a^{2} - 22 a - 123\) , \( -37 a^{2} + 70 a + 299\bigr] \) |
${y}^2+\left(a^{2}-2a-6\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}+\left(13a^{2}-22a-123\right){x}-37a^{2}+70a+299$ |
49.2-a6 |
49.2-a |
$6$ |
$8$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{10} \) |
$6.59607$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$45.41509929$ |
2.353872389 |
\( \frac{909723}{2401} a^{2} - \frac{2152223}{2401} a - \frac{2389809}{2401} \) |
\( \bigl[a^{2} - 2 a - 6\) , \( -a^{2} + 2 a + 5\) , \( a + 1\) , \( -2 a^{2} + 3 a + 17\) , \( -5 a^{2} + 8 a + 40\bigr] \) |
${y}^2+\left(a^{2}-2a-6\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}+\left(-2a^{2}+3a+17\right){x}-5a^{2}+8a+40$ |
49.2-b1 |
49.2-b |
$6$ |
$8$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
49.2 |
\( 7^{2} \) |
\( - 7^{8} \) |
$6.59607$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$64$ |
\( 2^{2} \) |
$1$ |
$0.938881352$ |
1.557196211 |
\( -\frac{28836360033558018913}{49} a^{2} + \frac{52590469545304245043}{49} a + \frac{245041987087172175919}{49} \) |
\( \bigl[a + 1\) , \( -a^{2} + 3 a + 7\) , \( a\) , \( 1312 a^{2} + 48 a - 20826\) , \( 91427 a^{2} - 55003 a - 1220094\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+3a+7\right){x}^{2}+\left(1312a^{2}+48a-20826\right){x}+91427a^{2}-55003a-1220094$ |
49.2-b2 |
49.2-b |
$6$ |
$8$ |
3.3.1489.1 |
$3$ |
$[3, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{10} \) |
$6.59607$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$30.04420326$ |
1.557196211 |
\( \frac{909723}{2401} a^{2} - \frac{2152223}{2401} a - \frac{2389809}{2401} \) |
\( \bigl[a + 1\) , \( -a^{2} + 3 a + 7\) , \( a\) , \( -8 a^{2} + 28 a + 34\) , \( -3 a^{2} + 17 a + 6\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+3a+7\right){x}^{2}+\left(-8a^{2}+28a+34\right){x}-3a^{2}+17a+6$ |
*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.