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 |
9.1-a1 |
9.1-a |
$4$ |
$6$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{4} \) |
$11.94063$ |
$(a^3-5a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1.746202949$ |
$70.38936677$ |
2.421160063 |
\( \frac{107659917118873597750}{9} a^{3} + \frac{41728339371778050850}{3} a^{2} - \frac{375211593784672264325}{9} a + \frac{49778440498971024902}{9} \) |
\( \bigl[a^{3} + a^{2} - 4 a\) , \( -a^{3} + 5 a - 3\) , \( 1\) , \( -34 a^{3} - 8 a^{2} + 201 a - 40\) , \( 32 a^{3} + 8 a^{2} - 187 a + 55\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+5a-3\right){x}^{2}+\left(-34a^{3}-8a^{2}+201a-40\right){x}+32a^{3}+8a^{2}-187a+55$ |
9.1-a2 |
9.1-a |
$4$ |
$6$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{12} \) |
$11.94063$ |
$(a^3-5a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$0.582067649$ |
$70.38936677$ |
2.421160063 |
\( \frac{674752222498342}{729} a^{3} - \frac{64476711587852}{81} a^{2} - \frac{4129749369310412}{729} a + \frac{4819876485854441}{729} \) |
\( \bigl[a^{3} - 5 a + 3\) , \( -a^{3} - a^{2} + 4 a + 2\) , \( a^{3} + a^{2} - 4 a - 1\) , \( -a^{3} - 11 a^{2} + a + 5\) , \( 5 a^{3} - 25 a^{2} - 17 a + 3\bigr] \) |
${y}^2+\left(a^{3}-5a+3\right){x}{y}+\left(a^{3}+a^{2}-4a-1\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+2\right){x}^{2}+\left(-a^{3}-11a^{2}+a+5\right){x}+5a^{3}-25a^{2}-17a+3$ |
9.1-a3 |
9.1-a |
$4$ |
$6$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$11.94063$ |
$(a^3-5a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$0.291033824$ |
$281.5574671$ |
2.421160063 |
\( -\frac{5235220976}{27} a^{3} - \frac{1449743636}{27} a^{2} + \frac{9848890172}{9} a - \frac{4158604241}{27} \) |
\( \bigl[a^{3} - 5 a + 3\) , \( -a^{3} - a^{2} + 4 a + 2\) , \( a^{3} + a^{2} - 4 a - 1\) , \( 4 a^{3} - a^{2} - 24 a + 10\) , \( 12 a^{3} + 2 a^{2} - 69 a + 11\bigr] \) |
${y}^2+\left(a^{3}-5a+3\right){x}{y}+\left(a^{3}+a^{2}-4a-1\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+2\right){x}^{2}+\left(4a^{3}-a^{2}-24a+10\right){x}+12a^{3}+2a^{2}-69a+11$ |
9.1-a4 |
9.1-a |
$4$ |
$6$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{2} \) |
$11.94063$ |
$(a^3-5a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.873101474$ |
$281.5574671$ |
2.421160063 |
\( -\frac{3573388000}{3} a^{3} - \frac{4105825225}{3} a^{2} + 4127976800 a - \frac{1643400016}{3} \) |
\( \bigl[a^{3} - 5 a + 4\) , \( -a^{2} - a + 4\) , \( a^{3} - 5 a + 3\) , \( -9 a^{3} - 15 a^{2} + 28 a + 7\) , \( -37 a^{3} - 45 a^{2} + 123 a - 7\bigr] \) |
${y}^2+\left(a^{3}-5a+4\right){x}{y}+\left(a^{3}-5a+3\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-9a^{3}-15a^{2}+28a+7\right){x}-37a^{3}-45a^{2}+123a-7$ |
9.1-b1 |
9.1-b |
$4$ |
$6$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{4} \) |
$11.94063$ |
$(a^3-5a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1.746202949$ |
$70.38936677$ |
2.421160063 |
\( \frac{145562890813235169625}{9} a^{3} - \frac{41728339371778050850}{3} a^{2} - \frac{890902445875871572550}{9} a + \frac{1039782488389394808377}{9} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 1\) , \( a^{2} - 5\) , \( a^{2} + 2 a - 4\) , \( 3 a^{3} + 9 a^{2} - 44 a + 9\) , \( -18 a^{3} - 12 a^{2} + 117 a - 22\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-1\right){x}{y}+\left(a^{2}+2a-4\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(3a^{3}+9a^{2}-44a+9\right){x}-18a^{3}-12a^{2}+117a-22$ |
9.1-b2 |
9.1-b |
$4$ |
$6$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{12} \) |
$11.94063$ |
$(a^3-5a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$0.582067649$ |
$70.38936677$ |
2.421160063 |
\( \frac{499054369970308}{729} a^{3} + \frac{64476711587852}{81} a^{2} - \frac{1739283593032838}{729} a + \frac{230750098235663}{729} \) |
\( \bigl[a^{3} - 5 a + 3\) , \( -a^{3} + a^{2} + 6 a - 8\) , \( a^{2} + a - 3\) , \( 8 a^{3} + 7 a^{2} - 41 a - 31\) , \( 31 a^{3} + 15 a^{2} - 166 a - 28\bigr] \) |
${y}^2+\left(a^{3}-5a+3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a-8\right){x}^{2}+\left(8a^{3}+7a^{2}-41a-31\right){x}+31a^{3}+15a^{2}-166a-28$ |
9.1-b3 |
9.1-b |
$4$ |
$6$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$11.94063$ |
$(a^3-5a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$0.291033824$ |
$281.5574671$ |
2.421160063 |
\( -\frac{414911704}{27} a^{3} + \frac{1449743636}{27} a^{2} - \frac{432002372}{9} a + \frac{154118123}{27} \) |
\( \bigl[a^{3} - 5 a + 3\) , \( -a^{3} + a^{2} + 6 a - 8\) , \( a^{2} + a - 3\) , \( 3 a^{3} - 3 a^{2} - 16 a + 14\) , \( -a^{3} - 2 a^{2} + 11 a - 8\bigr] \) |
${y}^2+\left(a^{3}-5a+3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a-8\right){x}^{2}+\left(3a^{3}-3a^{2}-16a+14\right){x}-a^{3}-2a^{2}+11a-8$ |
9.1-b4 |
9.1-b |
$4$ |
$6$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{2} \) |
$11.94063$ |
$(a^3-5a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.873101474$ |
$281.5574671$ |
2.421160063 |
\( -\frac{4950572375}{3} a^{3} + \frac{4105825225}{3} a^{2} + 10078623825 a - \frac{34515729716}{3} \) |
\( \bigl[a^{3} - 5 a + 4\) , \( a^{2} + a - 3\) , \( a^{3} - 5 a + 3\) , \( -11 a^{3} + 15 a^{2} + 72 a - 104\) , \( -54 a^{3} + 45 a^{2} + 332 a - 373\bigr] \) |
${y}^2+\left(a^{3}-5a+4\right){x}{y}+\left(a^{3}-5a+3\right){y}={x}^{3}+\left(a^{2}+a-3\right){x}^{2}+\left(-11a^{3}+15a^{2}+72a-104\right){x}-54a^{3}+45a^{2}+332a-373$ |
9.2-a1 |
9.2-a |
$2$ |
$5$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{30} \) |
$11.94063$ |
$(a^3-5a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3Ns, 5B.1.2 |
$25$ |
\( 1 \) |
$1$ |
$4.680761625$ |
1.152519450 |
\( \frac{3760877957808128}{14348907} a^{3} - \frac{18804389789040640}{14348907} a + \frac{5394071160094720}{4782969} \) |
\( \bigl[0\) , \( -a^{2} - a + 4\) , \( a^{3} - 6 a + 4\) , \( 13 a^{3} - 47 a^{2} + 40 a - 5\) , \( 845 a^{3} - 3012 a^{2} + 2715 a - 335\bigr] \) |
${y}^2+\left(a^{3}-6a+4\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(13a^{3}-47a^{2}+40a-5\right){x}+845a^{3}-3012a^{2}+2715a-335$ |
9.2-a2 |
9.2-a |
$2$ |
$5$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$11.94063$ |
$(a^3-5a+2)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3Ns, 5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2925.476015$ |
1.152519450 |
\( \frac{131072}{27} a^{3} - \frac{655360}{27} a + \frac{163840}{9} \) |
\( \bigl[0\) , \( -a^{2} - a + 4\) , \( a^{3} - 6 a + 4\) , \( -a^{3} - a^{2} + 4 a - 1\) , \( 2 a^{3} + 3 a^{2} - 6 a - 2\bigr] \) |
${y}^2+\left(a^{3}-6a+4\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-a^{3}-a^{2}+4a-1\right){x}+2a^{3}+3a^{2}-6a-2$ |
9.2-b1 |
9.2-b |
$1$ |
$1$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$11.94063$ |
$(a^3-5a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.031563682$ |
$614.7354933$ |
2.293236928 |
\( \frac{12573638656}{27} a^{3} - \frac{45038080000}{27} a^{2} + \frac{40844345344}{27} a - \frac{4869615616}{27} \) |
\( \bigl[0\) , \( a^{3} - 5 a + 3\) , \( 1\) , \( -a^{3} + a^{2} + 6 a - 8\) , \( -2 a^{3} + 2 a^{2} + 12 a - 17\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a^{3}-5a+3\right){x}^{2}+\left(-a^{3}+a^{2}+6a-8\right){x}-2a^{3}+2a^{2}+12a-17$ |
9.2-c1 |
9.2-c |
$1$ |
$1$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$11.94063$ |
$(a^3-5a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.031563682$ |
$614.7354933$ |
2.293236928 |
\( \frac{161324257280}{27} a^{3} + \frac{45038080000}{27} a^{2} - \frac{910333825024}{27} a + \frac{126115680256}{27} \) |
\( \bigl[0\) , \( a^{3} - 5 a + 3\) , \( 1\) , \( -a^{3} - a^{2} + 4 a - 1\) , \( -2 a^{3} - 2 a^{2} + 8 a - 3\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a^{3}-5a+3\right){x}^{2}+\left(-a^{3}-a^{2}+4a-1\right){x}-2a^{3}-2a^{2}+8a-3$ |
13.1-a1 |
13.1-a |
$1$ |
$1$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
13.1 |
\( 13 \) |
\( - 13^{3} \) |
$12.50230$ |
$(a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.025447258$ |
$902.9623705$ |
2.715711455 |
\( \frac{11173779}{169} a^{3} - \frac{9708841}{169} a^{2} - \frac{68219877}{169} a + \frac{79917143}{169} \) |
\( \bigl[a^{2} + 2 a - 4\) , \( -a^{2} - a + 5\) , \( a^{3} - 6 a + 4\) , \( 2 a^{3} - 8 a^{2} - 16 a + 31\) , \( -173 a^{3} - 205 a^{2} + 592 a - 60\bigr] \) |
${y}^2+\left(a^{2}+2a-4\right){x}{y}+\left(a^{3}-6a+4\right){y}={x}^{3}+\left(-a^{2}-a+5\right){x}^{2}+\left(2a^{3}-8a^{2}-16a+31\right){x}-173a^{3}-205a^{2}+592a-60$ |
13.1-b1 |
13.1-b |
$2$ |
$7$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
13.1 |
\( 13 \) |
\( 13^{7} \) |
$12.50230$ |
$(a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.3 |
$196$ |
\( 1 \) |
$1$ |
$0.415793724$ |
0.802649116 |
\( -\frac{1068358075329976592658}{28561} a^{3} + \frac{918794785753423236209}{28561} a^{2} + \frac{6538773839224138694636}{28561} a - \frac{7631478134401985725625}{28561} \) |
\( \bigl[a^{2} + 2 a - 3\) , \( a^{2} - 3\) , \( a^{3} + a^{2} - 5 a\) , \( -378 a^{3} + 439 a^{2} + 2364 a - 3325\) , \( -9140 a^{3} + 8645 a^{2} + 56270 a - 69674\bigr] \) |
${y}^2+\left(a^{2}+2a-3\right){x}{y}+\left(a^{3}+a^{2}-5a\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-378a^{3}+439a^{2}+2364a-3325\right){x}-9140a^{3}+8645a^{2}+56270a-69674$ |
13.1-b2 |
13.1-b |
$2$ |
$7$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
13.1 |
\( 13 \) |
\( 13 \) |
$12.50230$ |
$(a+1)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.1 |
$4$ |
\( 1 \) |
$1$ |
$998.3207327$ |
0.802649116 |
\( -\frac{6828}{13} a^{3} - \frac{5246}{13} a^{2} + \frac{30055}{13} a - \frac{4131}{13} \) |
\( \bigl[a^{2} + 2 a - 3\) , \( a^{2} - 3\) , \( a^{3} + a^{2} - 5 a\) , \( 2 a^{3} + 4 a^{2} - 6 a\) , \( 5 a^{3} + 6 a^{2} - 18 a + 1\bigr] \) |
${y}^2+\left(a^{2}+2a-3\right){x}{y}+\left(a^{3}+a^{2}-5a\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(2a^{3}+4a^{2}-6a\right){x}+5a^{3}+6a^{2}-18a+1$ |
13.2-a1 |
13.2-a |
$1$ |
$1$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
13.2 |
\( 13 \) |
\( - 13^{3} \) |
$12.50230$ |
$(a^3-6a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.025447258$ |
$902.9623705$ |
2.715711455 |
\( \frac{8531638}{169} a^{3} + \frac{9708841}{169} a^{2} - \frac{30307208}{169} a + \frac{4028833}{169} \) |
\( \bigl[a^{3} + a^{2} - 5 a\) , \( a^{3} - 5 a + 2\) , \( a^{3} + a^{2} - 4 a - 1\) , \( 2 a^{3} + 5 a^{2} - 10 a - 23\) , \( -245 a^{3} + 198 a^{2} + 1494 a - 1680\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a\right){x}{y}+\left(a^{3}+a^{2}-4a-1\right){y}={x}^{3}+\left(a^{3}-5a+2\right){x}^{2}+\left(2a^{3}+5a^{2}-10a-23\right){x}-245a^{3}+198a^{2}+1494a-1680$ |
13.2-b1 |
13.2-b |
$2$ |
$7$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
13.2 |
\( 13 \) |
\( 13^{7} \) |
$12.50230$ |
$(a^3-6a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.3 |
$196$ |
\( 1 \) |
$1$ |
$0.415793724$ |
0.802649116 |
\( -\frac{790169398509144097521}{28561} a^{3} - \frac{918794785753423236209}{28561} a^{2} + \frac{2753863529971464756259}{28561} a - \frac{365348603665525586751}{28561} \) |
\( \bigl[a^{3} + a^{2} - 5 a - 1\) , \( a^{3} + a^{2} - 4 a - 1\) , \( a^{3} + a^{2} - 4 a - 1\) , \( -343 a^{3} - 433 a^{2} + 1246 a - 175\) , \( -8215 a^{3} - 9808 a^{2} + 28998 a - 3855\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-1\right){x}{y}+\left(a^{3}+a^{2}-4a-1\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-1\right){x}^{2}+\left(-343a^{3}-433a^{2}+1246a-175\right){x}-8215a^{3}-9808a^{2}+28998a-3855$ |
13.2-b2 |
13.2-b |
$2$ |
$7$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
13.2 |
\( 13 \) |
\( 13 \) |
$12.50230$ |
$(a^3-6a+4)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.1 |
$4$ |
\( 1 \) |
$1$ |
$998.3207327$ |
0.802649116 |
\( -\frac{5667}{13} a^{3} + \frac{5246}{13} a^{2} + \frac{32420}{13} a - \frac{37370}{13} \) |
\( \bigl[a^{3} + a^{2} - 5 a - 1\) , \( a^{3} + a^{2} - 4 a - 1\) , \( a^{3} + a^{2} - 4 a - 1\) , \( 2 a^{3} + 2 a^{2} - 9 a\) , \( a^{3} + a^{2} - 4 a\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-1\right){x}{y}+\left(a^{3}+a^{2}-4a-1\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-1\right){x}^{2}+\left(2a^{3}+2a^{2}-9a\right){x}+a^{3}+a^{2}-4a$ |
16.1-a1 |
16.1-a |
$2$ |
$3$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$12.83104$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.113129354$ |
$613.0569866$ |
2.732296821 |
\( -516142647 a^{3} - \frac{1200260929}{2} a^{2} + \frac{3597610857}{2} a - 238643487 \) |
\( \bigl[a^{2} + 2 a - 4\) , \( a^{2} + a - 5\) , \( a + 1\) , \( 3 a^{3} - 15 a + 11\) , \( -2 a^{3} + 4 a^{2} + 15 a - 23\bigr] \) |
${y}^2+\left(a^{2}+2a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(3a^{3}-15a+11\right){x}-2a^{3}+4a^{2}+15a-23$ |
16.1-a2 |
16.1-a |
$2$ |
$3$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$12.83104$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.037709784$ |
$613.0569866$ |
2.732296821 |
\( -\frac{797575}{4} a^{3} + \frac{729565}{8} a^{2} + \frac{4735085}{4} a - \frac{7764949}{8} \) |
\( \bigl[a^{3} + a^{2} - 5 a\) , \( a - 1\) , \( a^{2} + a - 3\) , \( -3 a^{3} - 4 a^{2} + 9 a - 2\) , \( 7 a^{3} + 9 a^{2} - 23 a + 1\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-3a^{3}-4a^{2}+9a-2\right){x}+7a^{3}+9a^{2}-23a+1$ |
16.1-b1 |
16.1-b |
$1$ |
$1$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$12.83104$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$139.9614387$ |
1.378478917 |
\( 715122120068 a^{3} + \frac{399291528079}{2} a^{2} - 4035350003100 a + 559048439360 \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{2} + 3\) , \( a^{3} - 6 a + 4\) , \( 27 a^{3} - 10 a^{2} - 161 a + 120\) , \( -9 a^{3} - 20 a^{2} + 44 a + 89\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{3}-6a+4\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(27a^{3}-10a^{2}-161a+120\right){x}-9a^{3}-20a^{2}+44a+89$ |
16.1-c1 |
16.1-c |
$6$ |
$45$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{20} \) |
$12.83104$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3B, 5B.1.2 |
$1$ |
\( 5 \) |
$9.926832636$ |
$1.304759140$ |
2.551307312 |
\( -\frac{1250637664527933}{32} a^{3} + \frac{6253188322639665}{32} a - \frac{2690606637259811}{16} \) |
\( \bigl[1\) , \( 1\) , \( a^{3} - 5 a + 3\) , \( -29 a^{3} + 145 a - 85\) , \( -52 a^{3} + 260 a - 262\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-5a+3\right){y}={x}^{3}+{x}^{2}+\left(-29a^{3}+145a-85\right){x}-52a^{3}+260a-262$ |
16.1-c2 |
16.1-c |
$6$ |
$45$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$12.83104$ |
$(2)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3B, 5B.1.1 |
$1$ |
\( 1 \) |
$1.985366527$ |
$815.4744629$ |
2.551307312 |
\( \frac{461373}{2} a^{3} - \frac{2306865}{2} a + \frac{321323}{2} \) |
\( \bigl[1\) , \( 1\) , \( a^{3} - 5 a + 3\) , \( a^{3} - 5 a\) , \( -a^{3} + 5 a - 2\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-5a+3\right){y}={x}^{3}+{x}^{2}+\left(a^{3}-5a\right){x}-a^{3}+5a-2$ |
16.1-c3 |
16.1-c |
$6$ |
$45$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$12.83104$ |
$(2)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3B, 5B.1.1 |
$1$ |
\( 1 \) |
$1.985366527$ |
$815.4744629$ |
2.551307312 |
\( -\frac{461373}{2} a^{3} + \frac{2306865}{2} a - 992771 \) |
\( \bigl[1\) , \( 1\) , \( a^{3} - 5 a + 4\) , \( -2 a^{3} + 10 a - 8\) , \( 0\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-5a+4\right){y}={x}^{3}+{x}^{2}+\left(-2a^{3}+10a-8\right){x}$ |
16.1-c4 |
16.1-c |
$6$ |
$45$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{20} \) |
$12.83104$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3B, 5B.1.2 |
$1$ |
\( 5 \) |
$9.926832636$ |
$1.304759140$ |
2.551307312 |
\( \frac{1250637664527933}{32} a^{3} - \frac{6253188322639665}{32} a + \frac{871975048120043}{32} \) |
\( \bigl[1\) , \( 1\) , \( a^{3} - 5 a + 4\) , \( 28 a^{3} - 140 a + 57\) , \( 51 a^{3} - 255 a - 5\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-5a+4\right){y}={x}^{3}+{x}^{2}+\left(28a^{3}-140a+57\right){x}+51a^{3}-255a-5$ |
16.1-c5 |
16.1-c |
$6$ |
$45$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$12.83104$ |
$(2)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3Cs, 5B.1.1 |
$1$ |
\( 3 \) |
$0.661788842$ |
$815.4744629$ |
2.551307312 |
\( \frac{1331}{8} \) |
\( \bigl[a^{2} + 2 a - 3\) , \( -a^{3} + 6 a - 2\) , \( a^{3} + a^{2} - 5 a\) , \( 9 a^{3} - 5 a^{2} - 50 a + 61\) , \( 81 a^{3} - 63 a^{2} - 486 a + 558\bigr] \) |
${y}^2+\left(a^{2}+2a-3\right){x}{y}+\left(a^{3}+a^{2}-5a\right){y}={x}^{3}+\left(-a^{3}+6a-2\right){x}^{2}+\left(9a^{3}-5a^{2}-50a+61\right){x}+81a^{3}-63a^{2}-486a+558$ |
16.1-c6 |
16.1-c |
$6$ |
$45$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{60} \) |
$12.83104$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3Cs, 5B.1.2 |
$1$ |
\( 3 \cdot 5 \) |
$3.308944212$ |
$1.304759140$ |
2.551307312 |
\( -\frac{1680914269}{32768} \) |
\( \bigl[a^{3} - 5 a + 4\) , \( 1\) , \( 1\) , \( 75 a^{3} - 375 a + 53\) , \( 507 a^{3} - 2535 a + 351\bigr] \) |
${y}^2+\left(a^{3}-5a+4\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(75a^{3}-375a+53\right){x}+507a^{3}-2535a+351$ |
16.1-d1 |
16.1-d |
$1$ |
$1$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$12.83104$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 1 \) |
$1$ |
$216.0490599$ |
2.127865195 |
\( -\frac{4087435}{4} a^{3} + \frac{20437175}{4} a - \frac{6436163}{8} \) |
\( \bigl[a\) , \( a - 1\) , \( a^{3} + a^{2} - 4 a - 1\) , \( -2 a^{3} - 3 a^{2} + 13 a - 6\) , \( -4 a^{3} + 2 a^{2} + 6 a - 4\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}+a^{2}-4a-1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a^{3}-3a^{2}+13a-6\right){x}-4a^{3}+2a^{2}+6a-4$ |
16.1-e1 |
16.1-e |
$2$ |
$3$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$12.83104$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.037709784$ |
$613.0569866$ |
2.732296821 |
\( -\frac{830295}{8} a^{3} - \frac{729565}{8} a^{2} + \frac{2657055}{8} a - \frac{363429}{8} \) |
\( \bigl[a^{2} + 2 a - 4\) , \( -a^{2} - 2 a + 5\) , \( a\) , \( -2 a^{3} + a^{2} + 11 a - 12\) , \( 8 a^{3} - 7 a^{2} - 49 a + 57\bigr] \) |
${y}^2+\left(a^{2}+2a-4\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}-2a+5\right){x}^{2}+\left(-2a^{3}+a^{2}+11a-12\right){x}+8a^{3}-7a^{2}-49a+57$ |
16.1-e2 |
16.1-e |
$2$ |
$3$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$12.83104$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.113129354$ |
$613.0569866$ |
2.732296821 |
\( -697919989 a^{3} + \frac{1200260929}{2} a^{2} + \frac{8543015503}{2} a - \frac{9969777529}{2} \) |
\( \bigl[a^{3} + a^{2} - 5 a\) , \( a^{3} + a^{2} - 4 a\) , \( a^{3} - 6 a + 3\) , \( 5 a^{3} + 6 a^{2} - 17 a - 2\) , \( 6 a^{3} + 5 a^{2} - 23 a + 7\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a\right){x}{y}+\left(a^{3}-6a+3\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a\right){x}^{2}+\left(5a^{3}+6a^{2}-17a-2\right){x}+6a^{3}+5a^{2}-23a+7$ |
16.1-f1 |
16.1-f |
$1$ |
$1$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$12.83104$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$139.9614387$ |
1.378478917 |
\( \frac{111473906537}{2} a^{3} - \frac{399291528079}{2} a^{2} + \frac{362109272835}{2} a - 21586712762 \) |
\( \bigl[a^{2} + a - 3\) , \( a^{3} + a^{2} - 5 a - 1\) , \( a + 1\) , \( 10 a^{3} + 8 a^{2} - 27 a + 5\) , \( 10 a^{3} + 20 a^{2} - 49 a + 6\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-1\right){x}^{2}+\left(10a^{3}+8a^{2}-27a+5\right){x}+10a^{3}+20a^{2}-49a+6$ |
17.1-a1 |
17.1-a |
$2$ |
$2$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{6} \) |
$12.92864$ |
$(-a^2+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \) |
$1$ |
$419.2947433$ |
2.064815027 |
\( -\frac{373772006280088926}{24137569} a^{3} - \frac{104353125339505594}{24137569} a^{2} + \frac{124067630283310034}{1419857} a - \frac{292172251736196651}{24137569} \) |
\( \bigl[a^{2} + 2 a - 4\) , \( a^{3} + a^{2} - 5 a\) , \( a^{3} - 5 a + 4\) , \( 6 a^{3} + 2 a^{2} - 18 a + 9\) , \( -14 a^{3} - 19 a^{2} + 55 a - 10\bigr] \) |
${y}^2+\left(a^{2}+2a-4\right){x}{y}+\left(a^{3}-5a+4\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a\right){x}^{2}+\left(6a^{3}+2a^{2}-18a+9\right){x}-14a^{3}-19a^{2}+55a-10$ |
17.1-a2 |
17.1-a |
$2$ |
$2$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{3} \) |
$12.92864$ |
$(-a^2+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 1 \) |
$1$ |
$838.5894866$ |
2.064815027 |
\( \frac{303602996}{4913} a^{3} + \frac{171242372}{4913} a^{2} - \frac{109002704}{289} a + \frac{253065657}{4913} \) |
\( \bigl[a^{3} - 5 a + 3\) , \( a^{3} - 7 a + 4\) , \( 0\) , \( -2 a^{2} - 6 a + 7\) , \( -5 a^{3} - 4 a^{2} + 21 a\bigr] \) |
${y}^2+\left(a^{3}-5a+3\right){x}{y}={x}^{3}+\left(a^{3}-7a+4\right){x}^{2}+\left(-2a^{2}-6a+7\right){x}-5a^{3}-4a^{2}+21a$ |
17.1-b1 |
17.1-b |
$1$ |
$1$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( -17 \) |
$12.92864$ |
$(-a^2+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$158.2818296$ |
1.558916278 |
\( -\frac{2804242674}{17} a^{3} - \frac{783016885}{17} a^{2} + 930804461 a - \frac{2192167277}{17} \) |
\( \bigl[a^{2} + 2 a - 4\) , \( a^{3} - a^{2} - 7 a + 6\) , \( a^{2} + a - 3\) , \( -10 a^{3} - 17 a^{2} + 27 a + 15\) , \( -53 a^{3} - 68 a^{2} + 176 a - 3\bigr] \) |
${y}^2+\left(a^{2}+2a-4\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-7a+6\right){x}^{2}+\left(-10a^{3}-17a^{2}+27a+15\right){x}-53a^{3}-68a^{2}+176a-3$ |
17.1-c1 |
17.1-c |
$1$ |
$1$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{3} \) |
$12.92864$ |
$(-a^2+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3 \) |
$0.066219871$ |
$370.0643856$ |
2.896267042 |
\( -\frac{5753728}{4913} a^{3} - \frac{1397846}{4913} a^{2} + \frac{1945728}{289} a - \frac{4604037}{4913} \) |
\( \bigl[a^{3} + a^{2} - 5 a\) , \( a^{3} + a^{2} - 4 a - 1\) , \( a^{3} - 5 a + 3\) , \( 5 a^{3} + 5 a^{2} - 19 a + 4\) , \( 12 a^{3} + 14 a^{2} - 41 a + 4\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a\right){x}{y}+\left(a^{3}-5a+3\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-1\right){x}^{2}+\left(5a^{3}+5a^{2}-19a+4\right){x}+12a^{3}+14a^{2}-41a+4$ |
17.2-a1 |
17.2-a |
$2$ |
$2$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( - 17^{6} \) |
$12.92864$ |
$(a^2+a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \) |
$1$ |
$419.2947433$ |
2.064815027 |
\( -\frac{29129197524757384}{24137569} a^{3} + \frac{104353125339505594}{24137569} a^{2} - \frac{94643695792039028}{24137569} a + \frac{11284297153258817}{24137569} \) |
\( \bigl[a^{3} + a^{2} - 5 a\) , \( a^{3} + a^{2} - 6 a - 1\) , \( 0\) , \( 12 a^{3} + 2 a^{2} - 69 a + 24\) , \( -47 a^{3} + 26 a^{2} + 281 a - 252\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a\right){x}{y}={x}^{3}+\left(a^{3}+a^{2}-6a-1\right){x}^{2}+\left(12a^{3}+2a^{2}-69a+24\right){x}-47a^{3}+26a^{2}+281a-252$ |
17.2-a2 |
17.2-a |
$2$ |
$2$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( 17^{3} \) |
$12.92864$ |
$(a^2+a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 1 \) |
$1$ |
$838.5894866$ |
2.064815027 |
\( -\frac{202670364}{4913} a^{3} - \frac{171242372}{4913} a^{2} + \frac{1348382808}{4913} a - \frac{67057819}{4913} \) |
\( \bigl[a^{3} - 5 a + 3\) , \( -a^{3} + 7 a - 2\) , \( 0\) , \( -4 a^{3} + 2 a^{2} + 26 a - 19\) , \( -5 a^{3} + 4 a^{2} + 29 a - 28\bigr] \) |
${y}^2+\left(a^{3}-5a+3\right){x}{y}={x}^{3}+\left(-a^{3}+7a-2\right){x}^{2}+\left(-4a^{3}+2a^{2}+26a-19\right){x}-5a^{3}+4a^{2}+29a-28$ |
17.2-b1 |
17.2-b |
$1$ |
$1$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( -17 \) |
$12.92864$ |
$(a^2+a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$158.2818296$ |
1.558916278 |
\( -\frac{218763322}{17} a^{3} + \frac{783016885}{17} a^{2} - \frac{708645857}{17} a + \frac{83152584}{17} \) |
\( \bigl[a^{3} + a^{2} - 5 a\) , \( a^{3} - 7 a + 3\) , \( a + 1\) , \( -18 a^{3} + 13 a^{2} + 106 a - 113\) , \( -73 a^{3} + 63 a^{2} + 446 a - 523\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-7a+3\right){x}^{2}+\left(-18a^{3}+13a^{2}+106a-113\right){x}-73a^{3}+63a^{2}+446a-523$ |
17.2-c1 |
17.2-c |
$1$ |
$1$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( - 17^{3} \) |
$12.92864$ |
$(a^2+a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3 \) |
$0.066219871$ |
$370.0643856$ |
2.896267042 |
\( -\frac{47146}{4913} a^{3} + \frac{1397846}{4913} a^{2} - \frac{4073006}{4913} a + \frac{2730787}{4913} \) |
\( \bigl[a^{2} + 2 a - 4\) , \( a^{2} + a - 3\) , \( a^{3} + a^{2} - 5 a\) , \( 5 a^{3} + 2 a^{2} - 24 a + 16\) , \( 11 a^{3} - 56 a + 44\bigr] \) |
${y}^2+\left(a^{2}+2a-4\right){x}{y}+\left(a^{3}+a^{2}-5a\right){y}={x}^{3}+\left(a^{2}+a-3\right){x}^{2}+\left(5a^{3}+2a^{2}-24a+16\right){x}+11a^{3}-56a+44$ |
25.1-a1 |
25.1-a |
$4$ |
$6$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{4} \) |
$13.56717$ |
$(a^2-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$373.0889925$ |
1.837275020 |
\( \frac{1246340306134}{25} a^{3} + \frac{317232187229}{5} a^{2} - \frac{4009291282116}{25} a + \frac{526769657298}{25} \) |
\( \bigl[a^{3} + a^{2} - 5 a\) , \( -a^{3} + a^{2} + 7 a - 6\) , \( a^{3} + a^{2} - 5 a - 1\) , \( a^{3} - 26 a^{2} + 27 a + 4\) , \( -8 a^{3} + 59 a^{2} - 71 a + 4\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a\right){x}{y}+\left(a^{3}+a^{2}-5a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+7a-6\right){x}^{2}+\left(a^{3}-26a^{2}+27a+4\right){x}-8a^{3}+59a^{2}-71a+4$ |
25.1-a2 |
25.1-a |
$4$ |
$6$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{2} \) |
$13.56717$ |
$(a^2-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$746.1779850$ |
1.837275020 |
\( \frac{6658813}{5} a^{3} - \frac{4676746}{5} a^{2} - \frac{39588456}{5} a + \frac{43583169}{5} \) |
\( \bigl[a^{3} + a^{2} - 5 a\) , \( -a^{3} + a^{2} + 7 a - 6\) , \( a^{3} + a^{2} - 5 a - 1\) , \( a^{3} + 4 a^{2} - 13 a + 9\) , \( -2 a^{3} + 10 a^{2} - 7 a - 4\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a\right){x}{y}+\left(a^{3}+a^{2}-5a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+7a-6\right){x}^{2}+\left(a^{3}+4a^{2}-13a+9\right){x}-2a^{3}+10a^{2}-7a-4$ |
25.1-a3 |
25.1-a |
$4$ |
$6$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$13.56717$ |
$(a^2-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$746.1779850$ |
1.837275020 |
\( \frac{281956}{125} a^{3} - \frac{435596}{125} a^{2} - \frac{107248}{125} a + \frac{70237}{25} \) |
\( \bigl[a\) , \( -a^{3} - a^{2} + 5 a + 2\) , \( a\) , \( -3 a^{3} - 2 a^{2} + 16 a\) , \( -2 a^{3} - a^{2} + 11 a - 1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{3}-a^{2}+5a+2\right){x}^{2}+\left(-3a^{3}-2a^{2}+16a\right){x}-2a^{3}-a^{2}+11a-1$ |
25.1-a4 |
25.1-a |
$4$ |
$6$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{12} \) |
$13.56717$ |
$(a^2-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$373.0889925$ |
1.837275020 |
\( -\frac{1045812090808}{15625} a^{3} + \frac{3746074672838}{15625} a^{2} - \frac{3397251348696}{15625} a + \frac{81012735053}{3125} \) |
\( \bigl[a\) , \( -a^{3} - a^{2} + 5 a + 2\) , \( a\) , \( 2 a^{3} - 2 a^{2} - 14 a + 5\) , \( 16 a^{3} + 6 a^{2} - 86 a + 13\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{3}-a^{2}+5a+2\right){x}^{2}+\left(2a^{3}-2a^{2}-14a+5\right){x}+16a^{3}+6a^{2}-86a+13$ |
25.1-b1 |
25.1-b |
$1$ |
$1$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{2} \) |
$13.56717$ |
$(a^2-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.037907185$ |
$1795.724021$ |
2.681716438 |
\( -24619 a^{3} + \frac{436442}{5} a^{2} - \frac{375637}{5} a + \frac{24974}{5} \) |
\( \bigl[a^{3} - 5 a + 4\) , \( -a^{3} - a^{2} + 6 a\) , \( a^{3} + a^{2} - 4 a\) , \( -2 a^{3} - 3 a^{2} + 8 a + 4\) , \( -2 a^{3} + 4 a + 1\bigr] \) |
${y}^2+\left(a^{3}-5a+4\right){x}{y}+\left(a^{3}+a^{2}-4a\right){y}={x}^{3}+\left(-a^{3}-a^{2}+6a\right){x}^{2}+\left(-2a^{3}-3a^{2}+8a+4\right){x}-2a^{3}+4a+1$ |
25.1-c1 |
25.1-c |
$1$ |
$1$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$13.56717$ |
$(a^2-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$187.3356222$ |
1.845066813 |
\( \frac{961844}{125} a^{3} + \frac{1083673}{125} a^{2} - \frac{3619444}{125} a + \frac{320209}{125} \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{3} + a^{2} + 6 a - 8\) , \( a^{3} - 6 a + 3\) , \( 3 a^{3} - 17 a + 7\) , \( 2 a^{3} + a^{2} - 11 a - 1\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{3}-6a+3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a-8\right){x}^{2}+\left(3a^{3}-17a+7\right){x}+2a^{3}+a^{2}-11a-1$ |
25.2-a1 |
25.2-a |
$4$ |
$6$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{4} \) |
$13.56717$ |
$(a^3+a^2-5a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$373.0889925$ |
1.837275020 |
\( \frac{1882589618543}{25} a^{3} - \frac{317232187229}{5} a^{2} - \frac{11635358341269}{25} a + \frac{2707728829508}{5} \) |
\( \bigl[a^{2} + 2 a - 4\) , \( -a^{3} + a^{2} + 8 a - 8\) , \( a^{3} + a^{2} - 4 a\) , \( 58 a^{3} + 29 a^{2} - 318 a - 16\) , \( -127 a^{3} - 80 a^{2} + 704 a + 165\bigr] \) |
${y}^2+\left(a^{2}+2a-4\right){x}{y}+\left(a^{3}+a^{2}-4a\right){y}={x}^{3}+\left(-a^{3}+a^{2}+8a-8\right){x}^{2}+\left(58a^{3}+29a^{2}-318a-16\right){x}-127a^{3}-80a^{2}+704a+165$ |
25.2-a2 |
25.2-a |
$4$ |
$6$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{2} \) |
$13.56717$ |
$(a^3+a^2-5a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$746.1779850$ |
1.837275020 |
\( \frac{5041168}{5} a^{3} + \frac{4676746}{5} a^{2} - \frac{18911449}{5} a + \frac{5993012}{5} \) |
\( \bigl[a^{2} + 2 a - 4\) , \( -a^{3} + a^{2} + 8 a - 8\) , \( a^{3} + a^{2} - 4 a\) , \( -12 a^{3} - a^{2} + 72 a - 11\) , \( -28 a^{3} - 6 a^{2} + 165 a - 17\bigr] \) |
${y}^2+\left(a^{2}+2a-4\right){x}{y}+\left(a^{3}+a^{2}-4a\right){y}={x}^{3}+\left(-a^{3}+a^{2}+8a-8\right){x}^{2}+\left(-12a^{3}-a^{2}+72a-11\right){x}-28a^{3}-6a^{2}+165a-17$ |
25.2-a3 |
25.2-a |
$4$ |
$6$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{12} \) |
$13.56717$ |
$(a^3+a^2-5a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$373.0889925$ |
1.837275020 |
\( -\frac{13418198566382}{15625} a^{3} - \frac{3746074672838}{15625} a^{2} + \frac{75717304634646}{15625} a - \frac{10489573041591}{15625} \) |
\( \bigl[a^{3} - 6 a + 3\) , \( a^{2} - 5\) , \( 0\) , \( 4 a - 8\) , \( 4 a^{3} - 7 a^{2} - 18 a + 31\bigr] \) |
${y}^2+\left(a^{3}-6a+3\right){x}{y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(4a-8\right){x}+4a^{3}-7a^{2}-18a+31$ |
25.2-a4 |
25.2-a |
$4$ |
$6$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{6} \) |
$13.56717$ |
$(a^3+a^2-5a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$746.1779850$ |
1.837275020 |
\( \frac{2020084}{125} a^{3} + \frac{435596}{125} a^{2} - \frac{11402952}{125} a + \frac{2516397}{125} \) |
\( \bigl[a^{3} - 6 a + 3\) , \( a^{2} - 5\) , \( 0\) , \( -a + 2\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-6a+3\right){x}{y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(-a+2\right){x}$ |
25.2-b1 |
25.2-b |
$1$ |
$1$ |
4.4.10309.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{2} \) |
$13.56717$ |
$(a^3+a^2-5a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.037907185$ |
$1795.724021$ |
2.681716438 |
\( -\frac{1550649}{5} a^{3} - \frac{436442}{5} a^{2} + \frac{8744357}{5} a - \frac{1202594}{5} \) |
\( \bigl[a^{3} - 5 a + 4\) , \( a^{3} + a^{2} - 6 a - 1\) , \( a^{3} + a^{2} - 4 a - 1\) , \( -2 a\) , \( -7 a^{3} - 2 a^{2} + 38 a - 7\bigr] \) |
${y}^2+\left(a^{3}-5a+4\right){x}{y}+\left(a^{3}+a^{2}-4a-1\right){y}={x}^{3}+\left(a^{3}+a^{2}-6a-1\right){x}^{2}-2a{x}-7a^{3}-2a^{2}+38a-7$ |
*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.