| 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 |
| 4.1-a1 |
4.1-a |
$6$ |
$45$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{10} \) |
$10.89529$ |
$(a^3-a^2-5a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B.1.2, 5B.4.2 |
$9$ |
\( 5 \) |
$3.227465434$ |
$0.353820636$ |
2.004816315 |
\( -\frac{46866366404774471142406706382678508925}{8} a^{3} - 837204824113363505263545929366924088 a^{2} + \frac{81776852534182441962754365040569479719}{2} a + \frac{327944882292203164723438266897992960759}{8} \) |
\( \bigl[a^{2} - a - 4\) , \( a\) , \( a^{3} - 5 a - 5\) , \( 589 a^{3} + 152 a^{2} - 4327 a - 4831\) , \( 19288 a^{3} + 3575 a^{2} - 137422 a - 142859\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{3}-5a-5\right){y}={x}^{3}+a{x}^{2}+\left(589a^{3}+152a^{2}-4327a-4831\right){x}+19288a^{3}+3575a^{2}-137422a-142859$ |
| 4.1-a2 |
4.1-a |
$6$ |
$45$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{2} \) |
$10.89529$ |
$(a^3-a^2-5a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B.1.2, 5B.4.1 |
$9$ |
\( 1 \) |
$0.645493086$ |
$8.845515909$ |
2.004816315 |
\( -34209743891669426 a^{3} + \frac{85596887776772763}{2} a^{2} + \frac{371849567703010955}{2} a - \frac{54689211566783959}{2} \) |
\( \bigl[a^{2} - a - 4\) , \( a\) , \( a^{3} - 5 a - 5\) , \( -96 a^{3} + 122 a^{2} + 523 a - 91\) , \( -697 a^{3} + 877 a^{2} + 3789 a - 585\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{3}-5a-5\right){y}={x}^{3}+a{x}^{2}+\left(-96a^{3}+122a^{2}+523a-91\right){x}-697a^{3}+877a^{2}+3789a-585$ |
| 4.1-a3 |
4.1-a |
$6$ |
$45$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{30} \) |
$10.89529$ |
$(a^3-a^2-5a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3Cs.1.1, 5B.4.2 |
$1$ |
\( 3 \cdot 5 \) |
$1.075821811$ |
$28.65947154$ |
2.004816315 |
\( -\frac{266320696004661}{256} a^{3} + \frac{266320696004661}{256} a^{2} + \frac{1331603480023305}{256} a + \frac{90950209108247}{32} \) |
\( \bigl[a^{2} - a - 4\) , \( a\) , \( a^{3} - 5 a - 5\) , \( 29 a^{3} - 28 a^{2} - 147 a - 51\) , \( 12 a^{3} + 63 a^{2} - 206 a - 287\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{3}-5a-5\right){y}={x}^{3}+a{x}^{2}+\left(29a^{3}-28a^{2}-147a-51\right){x}+12a^{3}+63a^{2}-206a-287$ |
| 4.1-a4 |
4.1-a |
$6$ |
$45$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{2} \) |
$10.89529$ |
$(a^3-a^2-5a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B.1.1, 5B.4.1 |
$1$ |
\( 1 \) |
$0.645493086$ |
$716.4867886$ |
2.004816315 |
\( -\frac{4312559010154335}{2} a^{3} - 6432420491639788 a^{2} - 4094666867772510 a + \frac{1445659614068901}{2} \) |
\( \bigl[a^{2} - a - 4\) , \( a\) , \( a^{3} - 5 a - 5\) , \( -a^{3} - 23 a^{2} - 42 a - 11\) , \( 31 a^{3} + 124 a^{2} + 104 a - 24\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{3}-5a-5\right){y}={x}^{3}+a{x}^{2}+\left(-a^{3}-23a^{2}-42a-11\right){x}+31a^{3}+124a^{2}+104a-24$ |
| 4.1-a5 |
4.1-a |
$6$ |
$45$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{6} \) |
$10.89529$ |
$(a^3-a^2-5a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3Cs.1.1, 5B.4.1 |
$1$ |
\( 3 \) |
$0.215164362$ |
$716.4867886$ |
2.004816315 |
\( -\frac{580191}{4} a^{3} + \frac{580191}{4} a^{2} + \frac{2900955}{4} a - 104276 \) |
\( \bigl[a^{2} - a - 4\) , \( a\) , \( a^{3} - 5 a - 5\) , \( -a^{3} + 2 a^{2} + 3 a - 6\) , \( -2 a - 5\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{3}-5a-5\right){y}={x}^{3}+a{x}^{2}+\left(-a^{3}+2a^{2}+3a-6\right){x}-2a-5$ |
| 4.1-a6 |
4.1-a |
$6$ |
$45$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{10} \) |
$10.89529$ |
$(a^3-a^2-5a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B.1.1, 5B.4.2 |
$1$ |
\( 5 \) |
$3.227465434$ |
$28.65947154$ |
2.004816315 |
\( -\frac{15304699571819954343113231442255234483}{2} a^{3} + \frac{114782803284961196556967999586634839561}{8} a^{2} + \frac{213318413323541674723280700596219315409}{8} a - \frac{32650720809061143338121030438961921637}{8} \) |
\( \bigl[a^{2} - a - 4\) , \( a\) , \( a^{3} - 5 a - 5\) , \( 689 a^{3} - 1428 a^{2} - 2067 a + 249\) , \( -23344 a^{3} + 45467 a^{2} + 77118 a - 12191\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{3}-5a-5\right){y}={x}^{3}+a{x}^{2}+\left(689a^{3}-1428a^{2}-2067a+249\right){x}-23344a^{3}+45467a^{2}+77118a-12191$ |
| 4.1-b1 |
4.1-b |
$6$ |
$45$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{10} \) |
$10.89529$ |
$(a^3-a^2-5a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B.1.1, 5B.4.2 |
$1$ |
\( 5 \) |
$3.227465434$ |
$28.65947154$ |
2.004816315 |
\( -\frac{46866366404774471142406706382678508925}{8} a^{3} - 837204824113363505263545929366924088 a^{2} + \frac{81776852534182441962754365040569479719}{2} a + \frac{327944882292203164723438266897992960759}{8} \) |
\( \bigl[a^{3} - 6 a - 4\) , \( a^{3} - 6 a - 6\) , \( a^{3} - a^{2} - 5 a - 1\) , \( 589 a^{3} + 153 a^{2} - 4324 a - 4830\) , \( -18547 a^{3} - 3626 a^{2} + 131800 a + 137439\bigr] \) |
${y}^2+\left(a^{3}-6a-4\right){x}{y}+\left(a^{3}-a^{2}-5a-1\right){y}={x}^{3}+\left(a^{3}-6a-6\right){x}^{2}+\left(589a^{3}+153a^{2}-4324a-4830\right){x}-18547a^{3}-3626a^{2}+131800a+137439$ |
| 4.1-b2 |
4.1-b |
$6$ |
$45$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{2} \) |
$10.89529$ |
$(a^3-a^2-5a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B.1.1, 5B.4.1 |
$1$ |
\( 1 \) |
$0.645493086$ |
$716.4867886$ |
2.004816315 |
\( -34209743891669426 a^{3} + \frac{85596887776772763}{2} a^{2} + \frac{371849567703010955}{2} a - \frac{54689211566783959}{2} \) |
\( \bigl[a^{3} - 6 a - 4\) , \( a^{3} - 6 a - 6\) , \( a^{3} - a^{2} - 5 a - 1\) , \( -96 a^{3} + 123 a^{2} + 526 a - 90\) , \( 723 a^{3} - 903 a^{2} - 3931 a + 590\bigr] \) |
${y}^2+\left(a^{3}-6a-4\right){x}{y}+\left(a^{3}-a^{2}-5a-1\right){y}={x}^{3}+\left(a^{3}-6a-6\right){x}^{2}+\left(-96a^{3}+123a^{2}+526a-90\right){x}+723a^{3}-903a^{2}-3931a+590$ |
| 4.1-b3 |
4.1-b |
$6$ |
$45$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{30} \) |
$10.89529$ |
$(a^3-a^2-5a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3Cs.1.1, 5B.4.2 |
$1$ |
\( 3 \cdot 5 \) |
$1.075821811$ |
$28.65947154$ |
2.004816315 |
\( -\frac{266320696004661}{256} a^{3} + \frac{266320696004661}{256} a^{2} + \frac{1331603480023305}{256} a + \frac{90950209108247}{32} \) |
\( \bigl[a^{3} - 6 a - 4\) , \( a^{3} - 6 a - 6\) , \( a^{3} - a^{2} - 5 a - 1\) , \( 29 a^{3} - 27 a^{2} - 144 a - 50\) , \( -11 a^{3} - 34 a^{2} + 184 a + 207\bigr] \) |
${y}^2+\left(a^{3}-6a-4\right){x}{y}+\left(a^{3}-a^{2}-5a-1\right){y}={x}^{3}+\left(a^{3}-6a-6\right){x}^{2}+\left(29a^{3}-27a^{2}-144a-50\right){x}-11a^{3}-34a^{2}+184a+207$ |
| 4.1-b4 |
4.1-b |
$6$ |
$45$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{2} \) |
$10.89529$ |
$(a^3-a^2-5a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B.1.2, 5B.4.1 |
$9$ |
\( 1 \) |
$0.645493086$ |
$8.845515909$ |
2.004816315 |
\( -\frac{4312559010154335}{2} a^{3} - 6432420491639788 a^{2} - 4094666867772510 a + \frac{1445659614068901}{2} \) |
\( \bigl[a^{3} - 6 a - 4\) , \( a^{3} - 6 a - 6\) , \( a^{3} - a^{2} - 5 a - 1\) , \( -a^{3} - 22 a^{2} - 39 a - 10\) , \( -55 a^{3} - 195 a^{2} - 161 a + 14\bigr] \) |
${y}^2+\left(a^{3}-6a-4\right){x}{y}+\left(a^{3}-a^{2}-5a-1\right){y}={x}^{3}+\left(a^{3}-6a-6\right){x}^{2}+\left(-a^{3}-22a^{2}-39a-10\right){x}-55a^{3}-195a^{2}-161a+14$ |
| 4.1-b5 |
4.1-b |
$6$ |
$45$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{6} \) |
$10.89529$ |
$(a^3-a^2-5a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3Cs.1.1, 5B.4.1 |
$1$ |
\( 3 \) |
$0.215164362$ |
$716.4867886$ |
2.004816315 |
\( -\frac{580191}{4} a^{3} + \frac{580191}{4} a^{2} + \frac{2900955}{4} a - 104276 \) |
\( \bigl[a^{3} - 6 a - 4\) , \( a^{3} - 6 a - 6\) , \( a^{3} - a^{2} - 5 a - 1\) , \( -a^{3} + 3 a^{2} + 6 a - 5\) , \( a^{3} - a^{2} - 5 a\bigr] \) |
${y}^2+\left(a^{3}-6a-4\right){x}{y}+\left(a^{3}-a^{2}-5a-1\right){y}={x}^{3}+\left(a^{3}-6a-6\right){x}^{2}+\left(-a^{3}+3a^{2}+6a-5\right){x}+a^{3}-a^{2}-5a$ |
| 4.1-b6 |
4.1-b |
$6$ |
$45$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{10} \) |
$10.89529$ |
$(a^3-a^2-5a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B.1.2, 5B.4.2 |
$9$ |
\( 5 \) |
$3.227465434$ |
$0.353820636$ |
2.004816315 |
\( -\frac{15304699571819954343113231442255234483}{2} a^{3} + \frac{114782803284961196556967999586634839561}{8} a^{2} + \frac{213318413323541674723280700596219315409}{8} a - \frac{32650720809061143338121030438961921637}{8} \) |
\( \bigl[a^{3} - 6 a - 4\) , \( a^{3} - 6 a - 6\) , \( a^{3} - a^{2} - 5 a - 1\) , \( 689 a^{3} - 1427 a^{2} - 2064 a + 250\) , \( 22605 a^{3} - 44138 a^{2} - 74800 a + 11751\bigr] \) |
${y}^2+\left(a^{3}-6a-4\right){x}{y}+\left(a^{3}-a^{2}-5a-1\right){y}={x}^{3}+\left(a^{3}-6a-6\right){x}^{2}+\left(689a^{3}-1427a^{2}-2064a+250\right){x}+22605a^{3}-44138a^{2}-74800a+11751$ |
| 4.1-c1 |
4.1-c |
$6$ |
$45$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{2} \) |
$10.89529$ |
$(a^3-a^2-5a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.4.1 |
$9$ |
\( 1 \) |
$1$ |
$17.53722959$ |
1.539433102 |
\( -34209743891669426 a^{3} + \frac{85596887776772763}{2} a^{2} + \frac{371849567703010955}{2} a - \frac{54689211566783959}{2} \) |
\( \bigl[a^{3} - 5 a - 5\) , \( a^{3} - 2 a^{2} - 3 a + 4\) , \( a^{3} - a^{2} - 4 a\) , \( 37 a^{3} - 35 a^{2} - 174 a - 89\) , \( 49 a^{3} - 134 a^{2} - 66 a + 221\bigr] \) |
${y}^2+\left(a^{3}-5a-5\right){x}{y}+\left(a^{3}-a^{2}-4a\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+4\right){x}^{2}+\left(37a^{3}-35a^{2}-174a-89\right){x}+49a^{3}-134a^{2}-66a+221$ |
| 4.1-c2 |
4.1-c |
$6$ |
$45$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{2} \) |
$10.89529$ |
$(a^3-a^2-5a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.4.1 |
$9$ |
\( 1 \) |
$1$ |
$17.53722959$ |
1.539433102 |
\( -\frac{4312559010154335}{2} a^{3} - 6432420491639788 a^{2} - 4094666867772510 a + \frac{1445659614068901}{2} \) |
\( \bigl[a^{3} - 5 a - 4\) , \( a^{2} - 2 a - 5\) , \( a^{2} - 4\) , \( 46 a^{3} - 47 a^{2} - 223 a - 106\) , \( -36 a^{3} + 215 a^{2} - 110 a - 571\bigr] \) |
${y}^2+\left(a^{3}-5a-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(46a^{3}-47a^{2}-223a-106\right){x}-36a^{3}+215a^{2}-110a-571$ |
| 4.1-c3 |
4.1-c |
$6$ |
$45$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{6} \) |
$10.89529$ |
$(a^3-a^2-5a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3Cs, 5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$157.8350663$ |
1.539433102 |
\( -\frac{580191}{4} a^{3} + \frac{580191}{4} a^{2} + \frac{2900955}{4} a - 104276 \) |
\( \bigl[a^{3} - 5 a - 4\) , \( a^{2} - 2 a - 5\) , \( a^{2} - 4\) , \( a^{3} + 3 a^{2} - 3 a - 11\) , \( a^{3} + 4 a^{2} + 3 a - 5\bigr] \) |
${y}^2+\left(a^{3}-5a-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(a^{3}+3a^{2}-3a-11\right){x}+a^{3}+4a^{2}+3a-5$ |
| 4.1-c4 |
4.1-c |
$6$ |
$45$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{30} \) |
$10.89529$ |
$(a^3-a^2-5a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3Cs, 5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$157.8350663$ |
1.539433102 |
\( -\frac{266320696004661}{256} a^{3} + \frac{266320696004661}{256} a^{2} + \frac{1331603480023305}{256} a + \frac{90950209108247}{32} \) |
\( \bigl[a^{3} - a^{2} - 4 a - 1\) , \( a - 1\) , \( 1\) , \( 1949 a^{3} - 2435 a^{2} - 10586 a + 1554\) , \( 48278 a^{3} - 60389 a^{2} - 262368 a + 38590\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a-1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(1949a^{3}-2435a^{2}-10586a+1554\right){x}+48278a^{3}-60389a^{2}-262368a+38590$ |
| 4.1-c5 |
4.1-c |
$6$ |
$45$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{10} \) |
$10.89529$ |
$(a^3-a^2-5a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.4.2 |
$9$ |
\( 1 \) |
$1$ |
$17.53722959$ |
1.539433102 |
\( -\frac{46866366404774471142406706382678508925}{8} a^{3} - 837204824113363505263545929366924088 a^{2} + \frac{81776852534182441962754365040569479719}{2} a + \frac{327944882292203164723438266897992960759}{8} \) |
\( \bigl[1\) , \( -a + 1\) , \( a^{3} - a^{2} - 5 a - 1\) , \( 2253 a^{3} - 4398 a^{2} - 7394 a + 1117\) , \( -114542 a^{3} + 212243 a^{2} + 407642 a - 62220\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-a^{2}-5a-1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2253a^{3}-4398a^{2}-7394a+1117\right){x}-114542a^{3}+212243a^{2}+407642a-62220$ |
| 4.1-c6 |
4.1-c |
$6$ |
$45$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{10} \) |
$10.89529$ |
$(a^3-a^2-5a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.4.2 |
$9$ |
\( 1 \) |
$1$ |
$17.53722959$ |
1.539433102 |
\( -\frac{15304699571819954343113231442255234483}{2} a^{3} + \frac{114782803284961196556967999586634839561}{8} a^{2} + \frac{213318413323541674723280700596219315409}{8} a - \frac{32650720809061143338121030438961921637}{8} \) |
\( \bigl[1\) , \( -a^{3} + a^{2} + 6 a + 2\) , \( a^{3} - a^{2} - 5 a - 1\) , \( 1834 a^{3} + 311 a^{2} - 13041 a - 13479\) , \( -84208 a^{3} - 13493 a^{2} + 586108 a + 591353\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-a^{2}-5a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a+2\right){x}^{2}+\left(1834a^{3}+311a^{2}-13041a-13479\right){x}-84208a^{3}-13493a^{2}+586108a+591353$ |
| 4.1-d1 |
4.1-d |
$6$ |
$45$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{30} \) |
$10.89529$ |
$(a^3-a^2-5a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3Cs, 5B.1.2 |
$25$ |
\( 1 \) |
$1$ |
$5.203946933$ |
1.268908164 |
\( -\frac{266320696004661}{256} a^{3} + \frac{266320696004661}{256} a^{2} + \frac{1331603480023305}{256} a + \frac{90950209108247}{32} \) |
\( \bigl[a^{3} - 5 a - 4\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( a^{3} - a^{2} - 5 a - 1\) , \( 1947 a^{3} - 2429 a^{2} - 10567 a + 1563\) , \( -49250 a^{3} + 61634 a^{2} + 267701 a - 39371\bigr] \) |
${y}^2+\left(a^{3}-5a-4\right){x}{y}+\left(a^{3}-a^{2}-5a-1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+2\right){x}^{2}+\left(1947a^{3}-2429a^{2}-10567a+1563\right){x}-49250a^{3}+61634a^{2}+267701a-39371$ |
| 4.1-d2 |
4.1-d |
$6$ |
$45$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{10} \) |
$10.89529$ |
$(a^3-a^2-5a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.1.2 |
$225$ |
\( 1 \) |
$1$ |
$0.578216325$ |
1.268908164 |
\( -\frac{15304699571819954343113231442255234483}{2} a^{3} + \frac{114782803284961196556967999586634839561}{8} a^{2} + \frac{213318413323541674723280700596219315409}{8} a - \frac{32650720809061143338121030438961921637}{8} \) |
\( \bigl[a^{3} - a^{2} - 5 a - 1\) , \( a^{3} - a^{2} - 6 a\) , \( a^{3} - a^{2} - 5 a\) , \( 1836 a^{3} + 309 a^{2} - 13053 a - 13482\) , \( 86043 a^{3} + 13803 a^{2} - 599155 a - 604835\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a-1\right){x}{y}+\left(a^{3}-a^{2}-5a\right){y}={x}^{3}+\left(a^{3}-a^{2}-6a\right){x}^{2}+\left(1836a^{3}+309a^{2}-13053a-13482\right){x}+86043a^{3}+13803a^{2}-599155a-604835$ |
| 4.1-d3 |
4.1-d |
$6$ |
$45$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{10} \) |
$10.89529$ |
$(a^3-a^2-5a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.1.2 |
$225$ |
\( 1 \) |
$1$ |
$0.578216325$ |
1.268908164 |
\( -\frac{46866366404774471142406706382678508925}{8} a^{3} - 837204824113363505263545929366924088 a^{2} + \frac{81776852534182441962754365040569479719}{2} a + \frac{327944882292203164723438266897992960759}{8} \) |
\( \bigl[a^{3} - a^{2} - 5 a - 1\) , \( a + 1\) , \( a^{3} - a^{2} - 5 a\) , \( 2253 a^{3} - 4398 a^{2} - 7392 a + 1116\) , \( 116795 a^{3} - 216641 a^{2} - 415035 a + 63335\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a-1\right){x}{y}+\left(a^{3}-a^{2}-5a\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2253a^{3}-4398a^{2}-7392a+1116\right){x}+116795a^{3}-216641a^{2}-415035a+63335$ |
| 4.1-d4 |
4.1-d |
$6$ |
$45$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{2} \) |
$10.89529$ |
$(a^3-a^2-5a)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.1.1 |
$9$ |
\( 1 \) |
$1$ |
$361.3852036$ |
1.268908164 |
\( -\frac{4312559010154335}{2} a^{3} - 6432420491639788 a^{2} - 4094666867772510 a + \frac{1445659614068901}{2} \) |
\( \bigl[a^{3} - a^{2} - 4 a - 1\) , \( a^{3} - 6 a - 6\) , \( a^{3} - 6 a - 4\) , \( 43 a^{3} - 48 a^{2} - 206 a - 90\) , \( 45 a^{3} - 287 a^{2} + 192 a + 798\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a-1\right){x}{y}+\left(a^{3}-6a-4\right){y}={x}^{3}+\left(a^{3}-6a-6\right){x}^{2}+\left(43a^{3}-48a^{2}-206a-90\right){x}+45a^{3}-287a^{2}+192a+798$ |
| 4.1-d5 |
4.1-d |
$6$ |
$45$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{2} \) |
$10.89529$ |
$(a^3-a^2-5a)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.1.1 |
$9$ |
\( 1 \) |
$1$ |
$361.3852036$ |
1.268908164 |
\( -34209743891669426 a^{3} + \frac{85596887776772763}{2} a^{2} + \frac{371849567703010955}{2} a - \frac{54689211566783959}{2} \) |
\( \bigl[a\) , \( a^{2} - 2 a - 5\) , \( 1\) , \( 39 a^{3} - 35 a^{2} - 200 a - 120\) , \( -8 a^{3} + 142 a^{2} - 187 a - 471\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(39a^{3}-35a^{2}-200a-120\right){x}-8a^{3}+142a^{2}-187a-471$ |
| 4.1-d6 |
4.1-d |
$6$ |
$45$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{6} \) |
$10.89529$ |
$(a^3-a^2-5a)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3Cs, 5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$3252.466833$ |
1.268908164 |
\( -\frac{580191}{4} a^{3} + \frac{580191}{4} a^{2} + \frac{2900955}{4} a - 104276 \) |
\( \bigl[a\) , \( a^{2} - 2 a - 5\) , \( 1\) , \( -a^{3} + 5 a + 5\) , \( a + 1\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(-a^{3}+5a+5\right){x}+a+1$ |
| 36.1-a1 |
36.1-a |
$2$ |
$2$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{2} \) |
$14.33901$ |
$(a^3-a^2-5a), (a^3-a^2-5a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 11 \) |
$1$ |
$20.18912238$ |
2.166044874 |
\( \frac{19790001340417}{192} a^{3} - \frac{19790001340417}{192} a^{2} - \frac{98950006702085}{192} a + \frac{4947198382079}{48} \) |
\( \bigl[a^{2} - a - 4\) , \( a\) , \( a^{2} - 3\) , \( 853 a^{3} - 853 a^{2} - 4265 a - 2389\) , \( 2811 a^{3} - 20230 a^{2} + 16012 a + 57386\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+a{x}^{2}+\left(853a^{3}-853a^{2}-4265a-2389\right){x}+2811a^{3}-20230a^{2}+16012a+57386$ |
| 36.1-a2 |
36.1-a |
$2$ |
$2$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{44} \cdot 3^{4} \) |
$14.33901$ |
$(a^3-a^2-5a), (a^3-a^2-5a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 11 \) |
$1$ |
$20.18912238$ |
2.166044874 |
\( -\frac{805304833}{6144} a^{3} + \frac{805304833}{6144} a^{2} + \frac{4026524165}{6144} a - \frac{535300095}{2048} \) |
\( \bigl[a^{2} - a - 4\) , \( a\) , \( a^{2} - 3\) , \( 53 a^{3} - 53 a^{2} - 265 a - 149\) , \( 59 a^{3} - 294 a^{2} + 108 a + 714\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+a{x}^{2}+\left(53a^{3}-53a^{2}-265a-149\right){x}+59a^{3}-294a^{2}+108a+714$ |
| 36.1-b1 |
36.1-b |
$4$ |
$10$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{10} \) |
$14.33901$ |
$(a^3-a^2-5a), (a^3-a^2-5a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$4$ |
\( 5^{2} \) |
$1$ |
$10.62449958$ |
2.590632540 |
\( \frac{221644716336740306539}{216} a^{3} - \frac{221644716336740306539}{216} a^{2} - \frac{1108223581683701532695}{216} a + \frac{40563798396921485351}{54} \) |
\( \bigl[a^{3} - 6 a - 4\) , \( a^{3} - 6 a - 6\) , \( a^{2} - a - 3\) , \( -207 a^{3} + 209 a^{2} + 1035 a - 346\) , \( -2738 a^{3} + 3888 a^{2} + 16116 a - 1870\bigr] \) |
${y}^2+\left(a^{3}-6a-4\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{3}-6a-6\right){x}^{2}+\left(-207a^{3}+209a^{2}+1035a-346\right){x}-2738a^{3}+3888a^{2}+16116a-1870$ |
| 36.1-b2 |
36.1-b |
$4$ |
$10$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{2} \) |
$14.33901$ |
$(a^3-a^2-5a), (a^3-a^2-5a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$4$ |
\( 1 \) |
$1$ |
$265.6124895$ |
2.590632540 |
\( -\frac{1758101372999}{6} a^{3} + \frac{1758101372999}{6} a^{2} + \frac{8790506864995}{6} a + \frac{2401611155686}{3} \) |
\( \bigl[a^{3} - 6 a - 4\) , \( a^{3} - 6 a - 6\) , \( a^{2} - a - 3\) , \( 28 a^{3} - 26 a^{2} - 140 a - 81\) , \( -23 a^{3} + 126 a^{2} - 60 a - 318\bigr] \) |
${y}^2+\left(a^{3}-6a-4\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{3}-6a-6\right){x}^{2}+\left(28a^{3}-26a^{2}-140a-81\right){x}-23a^{3}+126a^{2}-60a-318$ |
| 36.1-b3 |
36.1-b |
$4$ |
$10$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{4} \) |
$14.33901$ |
$(a^3-a^2-5a), (a^3-a^2-5a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$265.6124895$ |
2.590632540 |
\( \frac{1744399}{6} a^{3} - \frac{1744399}{6} a^{2} - \frac{8721995}{6} a - \frac{4763501}{6} \) |
\( \bigl[a^{3} - 6 a - 4\) , \( a^{3} - 6 a - 6\) , \( a^{2} - a - 3\) , \( 3 a^{3} - a^{2} - 15 a - 11\) , \( 3 a^{2} - a - 6\bigr] \) |
${y}^2+\left(a^{3}-6a-4\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{3}-6a-6\right){x}^{2}+\left(3a^{3}-a^{2}-15a-11\right){x}+3a^{2}-a-6$ |
| 36.1-b4 |
36.1-b |
$4$ |
$10$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{20} \) |
$14.33901$ |
$(a^3-a^2-5a), (a^3-a^2-5a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2^{2} \cdot 5^{2} \) |
$1$ |
$10.62449958$ |
2.590632540 |
\( -\frac{4232167993969}{7776} a^{3} + \frac{4232167993969}{7776} a^{2} + \frac{21160839969845}{7776} a - \frac{38248782853}{96} \) |
\( \bigl[a^{3} - 6 a - 4\) , \( a^{3} - 6 a - 6\) , \( a^{2} - a - 3\) , \( -27 a^{3} + 29 a^{2} + 135 a + 14\) , \( -38 a^{3} + 36 a^{2} + 240 a + 2\bigr] \) |
${y}^2+\left(a^{3}-6a-4\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{3}-6a-6\right){x}^{2}+\left(-27a^{3}+29a^{2}+135a+14\right){x}-38a^{3}+36a^{2}+240a+2$ |
| 36.1-c1 |
36.1-c |
$2$ |
$2$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{2} \) |
$14.33901$ |
$(a^3-a^2-5a), (a^3-a^2-5a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$18.19551662$ |
0.177468678 |
\( \frac{19790001340417}{192} a^{3} - \frac{19790001340417}{192} a^{2} - \frac{98950006702085}{192} a + \frac{4947198382079}{48} \) |
\( \bigl[a^{3} - 5 a - 5\) , \( -a^{3} + 2 a^{2} + 3 a - 3\) , \( 1\) , \( -174 a^{3} - 678 a^{2} - 664 a - 160\) , \( -10427 a^{3} - 30124 a^{2} - 17695 a + 4480\bigr] \) |
${y}^2+\left(a^{3}-5a-5\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-3\right){x}^{2}+\left(-174a^{3}-678a^{2}-664a-160\right){x}-10427a^{3}-30124a^{2}-17695a+4480$ |
| 36.1-c2 |
36.1-c |
$2$ |
$2$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{44} \cdot 3^{4} \) |
$14.33901$ |
$(a^3-a^2-5a), (a^3-a^2-5a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$18.19551662$ |
0.177468678 |
\( -\frac{805304833}{6144} a^{3} + \frac{805304833}{6144} a^{2} + \frac{4026524165}{6144} a - \frac{535300095}{2048} \) |
\( \bigl[a^{3} - 5 a - 5\) , \( -a^{3} + 2 a^{2} + 3 a - 3\) , \( 1\) , \( -14 a^{3} - 38 a^{2} - 24 a\) , \( -187 a^{3} - 556 a^{2} - 351 a + 64\bigr] \) |
${y}^2+\left(a^{3}-5a-5\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-3\right){x}^{2}+\left(-14a^{3}-38a^{2}-24a\right){x}-187a^{3}-556a^{2}-351a+64$ |
| 36.1-d1 |
36.1-d |
$4$ |
$10$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{10} \) |
$14.33901$ |
$(a^3-a^2-5a), (a^3-a^2-5a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$4$ |
\( 1 \) |
$1$ |
$82.07769964$ |
0.800539010 |
\( \frac{221644716336740306539}{216} a^{3} - \frac{221644716336740306539}{216} a^{2} - \frac{1108223581683701532695}{216} a + \frac{40563798396921485351}{54} \) |
\( \bigl[a^{3} - 5 a - 5\) , \( a^{3} - 2 a^{2} - 3 a + 4\) , \( a^{3} - 5 a - 4\) , \( 731 a^{3} - 601 a^{2} - 4113 a - 2775\) , \( -5399 a^{3} + 5350 a^{2} + 28926 a + 17243\bigr] \) |
${y}^2+\left(a^{3}-5a-5\right){x}{y}+\left(a^{3}-5a-4\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+4\right){x}^{2}+\left(731a^{3}-601a^{2}-4113a-2775\right){x}-5399a^{3}+5350a^{2}+28926a+17243$ |
| 36.1-d2 |
36.1-d |
$4$ |
$10$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{20} \) |
$14.33901$ |
$(a^3-a^2-5a), (a^3-a^2-5a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$82.07769964$ |
0.800539010 |
\( -\frac{4232167993969}{7776} a^{3} + \frac{4232167993969}{7776} a^{2} + \frac{21160839969845}{7776} a - \frac{38248782853}{96} \) |
\( \bigl[a^{3} - 5 a - 5\) , \( a^{3} - 2 a^{2} - 3 a + 4\) , \( a^{3} - 5 a - 4\) , \( -169 a^{3} + 119 a^{2} + 927 a + 645\) , \( -1115 a^{3} + 310 a^{2} + 6966 a + 6047\bigr] \) |
${y}^2+\left(a^{3}-5a-5\right){x}{y}+\left(a^{3}-5a-4\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+4\right){x}^{2}+\left(-169a^{3}+119a^{2}+927a+645\right){x}-1115a^{3}+310a^{2}+6966a+6047$ |
| 36.1-d3 |
36.1-d |
$4$ |
$10$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{2} \) |
$14.33901$ |
$(a^3-a^2-5a), (a^3-a^2-5a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$4$ |
\( 1 \) |
$1$ |
$82.07769964$ |
0.800539010 |
\( -\frac{1758101372999}{6} a^{3} + \frac{1758101372999}{6} a^{2} + \frac{8790506864995}{6} a + \frac{2401611155686}{3} \) |
\( \bigl[a\) , \( -a^{3} + 7 a + 5\) , \( a^{2} - a - 4\) , \( -6 a^{3} - 18 a^{2} - 8 a + 5\) , \( 35 a^{3} + 92 a^{2} + 35 a - 31\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{3}+7a+5\right){x}^{2}+\left(-6a^{3}-18a^{2}-8a+5\right){x}+35a^{3}+92a^{2}+35a-31$ |
| 36.1-d4 |
36.1-d |
$4$ |
$10$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{4} \) |
$14.33901$ |
$(a^3-a^2-5a), (a^3-a^2-5a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$82.07769964$ |
0.800539010 |
\( \frac{1744399}{6} a^{3} - \frac{1744399}{6} a^{2} - \frac{8721995}{6} a - \frac{4763501}{6} \) |
\( \bigl[a\) , \( -a^{3} + 7 a + 5\) , \( a^{2} - a - 4\) , \( -a^{3} + 2 a^{2} + 12 a + 10\) , \( 3 a^{3} + 10 a^{2} + 9 a + 1\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{3}+7a+5\right){x}^{2}+\left(-a^{3}+2a^{2}+12a+10\right){x}+3a^{3}+10a^{2}+9a+1$ |
| 36.1-e1 |
36.1-e |
$4$ |
$10$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{2} \) |
$14.33901$ |
$(a^3-a^2-5a), (a^3-a^2-5a-1)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$4$ |
\( 1 \) |
$1$ |
$859.5513144$ |
0.335342906 |
\( -\frac{1758101372999}{6} a^{3} + \frac{1758101372999}{6} a^{2} + \frac{8790506864995}{6} a + \frac{2401611155686}{3} \) |
\( \bigl[a^{3} - 5 a - 5\) , \( -a^{3} + 2 a^{2} + 3 a - 3\) , \( a^{3} - 6 a - 5\) , \( -5 a^{3} - 14 a^{2} - 19 a - 12\) , \( -49 a^{3} - 147 a^{2} - 100 a + 9\bigr] \) |
${y}^2+\left(a^{3}-5a-5\right){x}{y}+\left(a^{3}-6a-5\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-3\right){x}^{2}+\left(-5a^{3}-14a^{2}-19a-12\right){x}-49a^{3}-147a^{2}-100a+9$ |
| 36.1-e2 |
36.1-e |
$4$ |
$10$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{4} \) |
$14.33901$ |
$(a^3-a^2-5a), (a^3-a^2-5a-1)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$859.5513144$ |
0.335342906 |
\( \frac{1744399}{6} a^{3} - \frac{1744399}{6} a^{2} - \frac{8721995}{6} a - \frac{4763501}{6} \) |
\( \bigl[a^{3} - 5 a - 5\) , \( -a^{3} + 2 a^{2} + 3 a - 3\) , \( a^{3} - 6 a - 5\) , \( 6 a^{2} + a - 7\) , \( -2 a^{3} + a - 3\bigr] \) |
${y}^2+\left(a^{3}-5a-5\right){x}{y}+\left(a^{3}-6a-5\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-3\right){x}^{2}+\left(6a^{2}+a-7\right){x}-2a^{3}+a-3$ |
| 36.1-e3 |
36.1-e |
$4$ |
$10$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{20} \) |
$14.33901$ |
$(a^3-a^2-5a), (a^3-a^2-5a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$25$ |
\( 2^{2} \) |
$1$ |
$1.375282103$ |
0.335342906 |
\( -\frac{4232167993969}{7776} a^{3} + \frac{4232167993969}{7776} a^{2} + \frac{21160839969845}{7776} a - \frac{38248782853}{96} \) |
\( \bigl[a\) , \( a^{2} - 2 a - 5\) , \( a^{3} - 6 a - 5\) , \( -168 a^{3} + 118 a^{2} + 910 a + 625\) , \( 897 a^{3} - 334 a^{2} - 5509 a - 4613\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-6a-5\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(-168a^{3}+118a^{2}+910a+625\right){x}+897a^{3}-334a^{2}-5509a-4613$ |
| 36.1-e4 |
36.1-e |
$4$ |
$10$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{10} \) |
$14.33901$ |
$(a^3-a^2-5a), (a^3-a^2-5a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$100$ |
\( 1 \) |
$1$ |
$1.375282103$ |
0.335342906 |
\( \frac{221644716336740306539}{216} a^{3} - \frac{221644716336740306539}{216} a^{2} - \frac{1108223581683701532695}{216} a + \frac{40563798396921485351}{54} \) |
\( \bigl[a\) , \( a^{2} - 2 a - 5\) , \( a^{3} - 6 a - 5\) , \( 732 a^{3} - 602 a^{2} - 4130 a - 2795\) , \( 6261 a^{3} - 5554 a^{2} - 35569 a - 23549\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-6a-5\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(732a^{3}-602a^{2}-4130a-2795\right){x}+6261a^{3}-5554a^{2}-35569a-23549$ |
| 36.1-f1 |
36.1-f |
$2$ |
$2$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{2} \) |
$14.33901$ |
$(a^3-a^2-5a), (a^3-a^2-5a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$36$ |
\( 1 \) |
$1$ |
$22.40115909$ |
1.966393018 |
\( \frac{19790001340417}{192} a^{3} - \frac{19790001340417}{192} a^{2} - \frac{98950006702085}{192} a + \frac{4947198382079}{48} \) |
\( \bigl[a^{3} - a^{2} - 4 a - 1\) , \( a - 1\) , \( a^{3} - a^{2} - 5 a - 1\) , \( -3412 a^{3} + 4266 a^{2} + 18598 a - 2902\) , \( 154536 a^{3} - 193381 a^{2} - 839438 a + 122653\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a-1\right){x}{y}+\left(a^{3}-a^{2}-5a-1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-3412a^{3}+4266a^{2}+18598a-2902\right){x}+154536a^{3}-193381a^{2}-839438a+122653$ |
| 36.1-f2 |
36.1-f |
$2$ |
$2$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{44} \cdot 3^{4} \) |
$14.33901$ |
$(a^3-a^2-5a), (a^3-a^2-5a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$9$ |
\( 2^{2} \) |
$1$ |
$22.40115909$ |
1.966393018 |
\( -\frac{805304833}{6144} a^{3} + \frac{805304833}{6144} a^{2} + \frac{4026524165}{6144} a - \frac{535300095}{2048} \) |
\( \bigl[a^{3} - a^{2} - 4 a - 1\) , \( a - 1\) , \( a^{3} - a^{2} - 5 a - 1\) , \( -212 a^{3} + 266 a^{2} + 1158 a - 182\) , \( 2536 a^{3} - 3173 a^{2} - 13774 a + 2013\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a-1\right){x}{y}+\left(a^{3}-a^{2}-5a-1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-212a^{3}+266a^{2}+1158a-182\right){x}+2536a^{3}-3173a^{2}-13774a+2013$ |
| 36.1-g1 |
36.1-g |
$4$ |
$10$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{10} \) |
$14.33901$ |
$(a^3-a^2-5a), (a^3-a^2-5a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$4$ |
\( 5^{2} \) |
$1$ |
$10.62449958$ |
2.590632540 |
\( \frac{221644716336740306539}{216} a^{3} - \frac{221644716336740306539}{216} a^{2} - \frac{1108223581683701532695}{216} a + \frac{40563798396921485351}{54} \) |
\( \bigl[a^{2} - a - 4\) , \( a\) , \( a^{3} - a^{2} - 4 a - 1\) , \( -209 a^{3} + 209 a^{2} + 1045 a - 337\) , \( 2739 a^{3} - 4097 a^{2} - 16666 a + 1739\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{3}-a^{2}-4a-1\right){y}={x}^{3}+a{x}^{2}+\left(-209a^{3}+209a^{2}+1045a-337\right){x}+2739a^{3}-4097a^{2}-16666a+1739$ |
| 36.1-g2 |
36.1-g |
$4$ |
$10$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{2} \) |
$14.33901$ |
$(a^3-a^2-5a), (a^3-a^2-5a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$4$ |
\( 1 \) |
$1$ |
$265.6124895$ |
2.590632540 |
\( -\frac{1758101372999}{6} a^{3} + \frac{1758101372999}{6} a^{2} + \frac{8790506864995}{6} a + \frac{2401611155686}{3} \) |
\( \bigl[a^{2} - a - 4\) , \( a\) , \( a^{3} - a^{2} - 4 a - 1\) , \( 26 a^{3} - 26 a^{2} - 130 a - 72\) , \( 24 a^{3} - 100 a^{2} + 10 a + 217\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{3}-a^{2}-4a-1\right){y}={x}^{3}+a{x}^{2}+\left(26a^{3}-26a^{2}-130a-72\right){x}+24a^{3}-100a^{2}+10a+217$ |
| 36.1-g3 |
36.1-g |
$4$ |
$10$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{4} \) |
$14.33901$ |
$(a^3-a^2-5a), (a^3-a^2-5a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$265.6124895$ |
2.590632540 |
\( \frac{1744399}{6} a^{3} - \frac{1744399}{6} a^{2} - \frac{8721995}{6} a - \frac{4763501}{6} \) |
\( \bigl[a^{2} - a - 4\) , \( a\) , \( a^{3} - a^{2} - 4 a - 1\) , \( a^{3} - a^{2} - 5 a - 2\) , \( a^{3} - 2 a^{2} - 4 a\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{3}-a^{2}-4a-1\right){y}={x}^{3}+a{x}^{2}+\left(a^{3}-a^{2}-5a-2\right){x}+a^{3}-2a^{2}-4a$ |
| 36.1-g4 |
36.1-g |
$4$ |
$10$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{20} \) |
$14.33901$ |
$(a^3-a^2-5a), (a^3-a^2-5a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2^{2} \cdot 5^{2} \) |
$1$ |
$10.62449958$ |
2.590632540 |
\( -\frac{4232167993969}{7776} a^{3} + \frac{4232167993969}{7776} a^{2} + \frac{21160839969845}{7776} a - \frac{38248782853}{96} \) |
\( \bigl[a^{2} - a - 4\) , \( a\) , \( a^{3} - a^{2} - 4 a - 1\) , \( -29 a^{3} + 29 a^{2} + 145 a + 23\) , \( 39 a^{3} - 65 a^{2} - 250 a + 47\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{3}-a^{2}-4a-1\right){y}={x}^{3}+a{x}^{2}+\left(-29a^{3}+29a^{2}+145a+23\right){x}+39a^{3}-65a^{2}-250a+47$ |
| 36.1-h1 |
36.1-h |
$2$ |
$2$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{2} \) |
$14.33901$ |
$(a^3-a^2-5a), (a^3-a^2-5a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 11 \) |
$1$ |
$20.18912238$ |
2.166044874 |
\( \frac{19790001340417}{192} a^{3} - \frac{19790001340417}{192} a^{2} - \frac{98950006702085}{192} a + \frac{4947198382079}{48} \) |
\( \bigl[a^{3} - 6 a - 4\) , \( a^{3} - 6 a - 6\) , \( 1\) , \( 853 a^{3} - 852 a^{2} - 4262 a - 2387\) , \( -2811 a^{3} + 21084 a^{2} - 17546 a - 60628\bigr] \) |
${y}^2+\left(a^{3}-6a-4\right){x}{y}+{y}={x}^{3}+\left(a^{3}-6a-6\right){x}^{2}+\left(853a^{3}-852a^{2}-4262a-2387\right){x}-2811a^{3}+21084a^{2}-17546a-60628$ |
| 36.1-h2 |
36.1-h |
$2$ |
$2$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{44} \cdot 3^{4} \) |
$14.33901$ |
$(a^3-a^2-5a), (a^3-a^2-5a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 11 \) |
$1$ |
$20.18912238$ |
2.166044874 |
\( -\frac{805304833}{6144} a^{3} + \frac{805304833}{6144} a^{2} + \frac{4026524165}{6144} a - \frac{535300095}{2048} \) |
\( \bigl[a^{3} - 6 a - 4\) , \( a^{3} - 6 a - 6\) , \( 1\) , \( 53 a^{3} - 52 a^{2} - 262 a - 147\) , \( -59 a^{3} + 348 a^{2} - 202 a - 916\bigr] \) |
${y}^2+\left(a^{3}-6a-4\right){x}{y}+{y}={x}^{3}+\left(a^{3}-6a-6\right){x}^{2}+\left(53a^{3}-52a^{2}-262a-147\right){x}-59a^{3}+348a^{2}-202a-916$ |
| 37.1-a1 |
37.1-a |
$4$ |
$6$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
37.1 |
\( 37 \) |
\( 37^{3} \) |
$14.38820$ |
$(a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 3 \) |
$3.749312226$ |
$8.952361846$ |
3.928509481 |
\( -\frac{4155745669800443116975209848815}{50653} a^{3} + \frac{7791857257318091093305793370801}{50653} a^{2} + \frac{14480798337431720961859809989470}{50653} a - \frac{2216444873376625079762636975885}{50653} \) |
\( \bigl[a + 1\) , \( a^{3} - 5 a - 5\) , \( a^{2} - a - 4\) , \( 352 a^{3} + 54 a^{2} - 2455 a - 2488\) , \( -2020 a^{3} - 285 a^{2} + 14088 a + 14085\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{3}-5a-5\right){x}^{2}+\left(352a^{3}+54a^{2}-2455a-2488\right){x}-2020a^{3}-285a^{2}+14088a+14085$ |
| 37.1-a2 |
37.1-a |
$4$ |
$6$ |
4.4.10512.1 |
$4$ |
$[4, 0]$ |
37.1 |
\( 37 \) |
\( 37 \) |
$14.38820$ |
$(a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1.249770742$ |
$80.57125662$ |
3.928509481 |
\( -\frac{1234239553}{37} a^{3} + \frac{20463157332}{37} a^{2} + \frac{26028147039}{37} a - \frac{1869517127}{37} \) |
\( \bigl[a + 1\) , \( a^{3} - 5 a - 5\) , \( a^{2} - a - 4\) , \( 217 a^{3} + 34 a^{2} - 1515 a - 1528\) , \( 3150 a^{3} + 446 a^{2} - 21991 a - 22038\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{3}-5a-5\right){x}^{2}+\left(217a^{3}+34a^{2}-1515a-1528\right){x}+3150a^{3}+446a^{2}-21991a-22038$ |
*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.
