| 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 |
| 11.2-a1 |
11.2-a |
$2$ |
$2$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( - 11^{4} \) |
$12.76038$ |
$(a^3-2a^2-3a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.125436291$ |
$744.7156759$ |
3.531204358 |
\( -\frac{18910807005341915}{14641} a^{3} + \frac{67187881938993500}{14641} a^{2} - \frac{28691642942948023}{14641} a - \frac{12177808500975501}{14641} \) |
\( \bigl[a^{2} - 2 a - 1\) , \( -a\) , \( a^{3} - a^{2} - 5 a + 1\) , \( -9 a^{3} + 15 a^{2} + 35 a - 8\) , \( 6 a^{3} - 11 a^{2} - 25 a + 17\bigr] \) |
${y}^2+\left(a^{2}-2a-1\right){x}{y}+\left(a^{3}-a^{2}-5a+1\right){y}={x}^{3}-a{x}^{2}+\left(-9a^{3}+15a^{2}+35a-8\right){x}+6a^{3}-11a^{2}-25a+17$ |
| 11.2-a2 |
11.2-a |
$2$ |
$2$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{2} \) |
$12.76038$ |
$(a^3-2a^2-3a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.062718145$ |
$2978.862703$ |
3.531204358 |
\( \frac{43447215}{121} a^{3} - \frac{123668230}{121} a^{2} + \frac{48403622}{121} a + \frac{21182783}{121} \) |
\( \bigl[a^{2} - 2 a - 1\) , \( -a\) , \( a^{3} - a^{2} - 5 a + 1\) , \( a^{3} - 10 a - 3\) , \( 2 a^{2} - 4 a - 2\bigr] \) |
${y}^2+\left(a^{2}-2a-1\right){x}{y}+\left(a^{3}-a^{2}-5a+1\right){y}={x}^{3}-a{x}^{2}+\left(a^{3}-10a-3\right){x}+2a^{2}-4a-2$ |
| 11.2-b1 |
11.2-b |
$2$ |
$2$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{2} \) |
$12.76038$ |
$(a^3-2a^2-3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$243.8485001$ |
1.152230199 |
\( \frac{43447215}{121} a^{3} - \frac{123668230}{121} a^{2} + \frac{48403622}{121} a + \frac{21182783}{121} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 2\) , \( a + 1\) , \( a + 1\) , \( 5 a^{3} - 5 a^{2} - 21 a - 5\) , \( 5 a^{3} - 5 a^{2} - 19 a - 5\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(5a^{3}-5a^{2}-21a-5\right){x}+5a^{3}-5a^{2}-19a-5$ |
| 11.2-b2 |
11.2-b |
$2$ |
$2$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( - 11^{4} \) |
$12.76038$ |
$(a^3-2a^2-3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$60.96212503$ |
1.152230199 |
\( -\frac{18910807005341915}{14641} a^{3} + \frac{67187881938993500}{14641} a^{2} - \frac{28691642942948023}{14641} a - \frac{12177808500975501}{14641} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 2\) , \( a + 1\) , \( a + 1\) , \( -15 a^{3} + 10 a^{2} + 104 a + 15\) , \( 11 a^{3} - 51 a^{2} + 64 a - 3\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-15a^{3}+10a^{2}+104a+15\right){x}+11a^{3}-51a^{2}+64a-3$ |
| 21.1-a1 |
21.1-a |
$6$ |
$8$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{32} \cdot 7^{4} \) |
$13.83461$ |
$(-a-1), (-a^3+2a^2+3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$64$ |
\( 2^{2} \) |
$1$ |
$2.244352954$ |
1.357438902 |
\( \frac{93351032504292897897277178575777}{4449101473433270241} a^{3} + \frac{10048303108249112395936794750967}{494344608159252249} a^{2} - \frac{104925144694088217346797735597220}{4449101473433270241} a - \frac{31444454475335045120254874254073}{4449101473433270241} \) |
\( \bigl[a^{3} - a^{2} - 5 a + 1\) , \( -a^{3} + 3 a^{2} + a - 5\) , \( a^{3} - a^{2} - 5 a + 1\) , \( -25 a^{3} + 96 a^{2} + 20 a - 279\) , \( 9074 a^{3} - 20228 a^{2} - 31398 a + 34017\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a+1\right){x}{y}+\left(a^{3}-a^{2}-5a+1\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+a-5\right){x}^{2}+\left(-25a^{3}+96a^{2}+20a-279\right){x}+9074a^{3}-20228a^{2}-31398a+34017$ |
| 21.1-a2 |
21.1-a |
$6$ |
$8$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{8} \cdot 7^{16} \) |
$13.83461$ |
$(-a-1), (-a^3+2a^2+3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$64$ |
\( 2^{2} \) |
$1$ |
$2.244352954$ |
1.357438902 |
\( -\frac{24324218882503346989897710983905}{218041257467152161} a^{3} + \frac{3130257293012684239299241034057}{24226806385239129} a^{2} + \frac{121012324553366544649411945327012}{218041257467152161} a + \frac{28895491954981087218640032315401}{218041257467152161} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( -a^{3} + a^{2} + 4 a + 1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( 308 a^{3} - 383 a^{2} - 1492 a - 365\) , \( 5525 a^{3} - 6544 a^{2} - 27301 a - 6514\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a+1\right){x}^{2}+\left(308a^{3}-383a^{2}-1492a-365\right){x}+5525a^{3}-6544a^{2}-27301a-6514$ |
| 21.1-a3 |
21.1-a |
$6$ |
$8$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{4} \cdot 7^{2} \) |
$13.83461$ |
$(-a-1), (-a^3+2a^2+3a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$143.6385890$ |
1.357438902 |
\( \frac{61454322416307957850243}{3969} a^{3} - \frac{15416010144890769909917}{441} a^{2} - \frac{210065945504149286427793}{3969} a + \frac{238492406894076670004716}{3969} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( -a^{3} + a^{2} + 4 a + 1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( -17 a^{3} + 27 a^{2} + 93 a - 65\) , \( 42 a^{3} - 73 a^{2} - 231 a + 220\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a+1\right){x}^{2}+\left(-17a^{3}+27a^{2}+93a-65\right){x}+42a^{3}-73a^{2}-231a+220$ |
| 21.1-a4 |
21.1-a |
$6$ |
$8$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{16} \cdot 7^{8} \) |
$13.83461$ |
$(-a-1), (-a^3+2a^2+3a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{2} \) |
$1$ |
$35.90964726$ |
1.357438902 |
\( -\frac{898589086686668844035}{248155780267521} a^{3} + \frac{163263946637405265181}{27572864474169} a^{2} + \frac{5263861833193040745233}{248155780267521} a + \frac{1266420698110974585316}{248155780267521} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( -a^{3} + a^{2} + 4 a + 1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( 13 a^{3} - 23 a^{2} - 77 a - 25\) , \( 94 a^{3} - 155 a^{2} - 543 a - 126\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a+1\right){x}^{2}+\left(13a^{3}-23a^{2}-77a-25\right){x}+94a^{3}-155a^{2}-543a-126$ |
| 21.1-a5 |
21.1-a |
$6$ |
$8$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{8} \cdot 7^{4} \) |
$13.83461$ |
$(-a-1), (-a^3+2a^2+3a-1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$574.5543562$ |
1.357438902 |
\( \frac{28918283118570229}{15752961} a^{3} - \frac{7254230548458608}{1750329} a^{2} - \frac{98850186870630073}{15752961} a + \frac{112226650825052689}{15752961} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( -a^{3} + a^{2} + 4 a + 1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( -2 a^{3} + 2 a^{2} + 8 a - 5\) , \( 2 a^{3} - 4 a^{2} - 13 a - 1\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a+1\right){x}^{2}+\left(-2a^{3}+2a^{2}+8a-5\right){x}+2a^{3}-4a^{2}-13a-1$ |
| 21.1-a6 |
21.1-a |
$6$ |
$8$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{4} \cdot 7^{2} \) |
$13.83461$ |
$(-a-1), (-a^3+2a^2+3a-1)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2298.217424$ |
1.357438902 |
\( -\frac{85319533}{3969} a^{3} + \frac{20933642}{441} a^{2} + \frac{307507810}{3969} a - \frac{296298013}{3969} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( -a^{3} + a^{2} + 4 a + 1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( -2 a^{3} + 2 a^{2} + 8 a\) , \( -a^{3} + a^{2} + 4 a\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a+1\right){x}^{2}+\left(-2a^{3}+2a^{2}+8a\right){x}-a^{3}+a^{2}+4a$ |
| 21.1-b1 |
21.1-b |
$2$ |
$3$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{3} \cdot 7 \) |
$13.83461$ |
$(-a-1), (-a^3+2a^2+3a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.130708535$ |
$231.7209466$ |
3.434785735 |
\( -\frac{80102}{189} a^{3} + \frac{24688}{21} a^{2} + \frac{201113}{189} a - \frac{284156}{189} \) |
\( \bigl[a^{2} - 2 a - 1\) , \( a^{3} - 3 a^{2} - a + 3\) , \( a^{3} - a^{2} - 4 a + 1\) , \( -2 a\) , \( -a^{3} + a^{2} + 4 a - 5\bigr] \) |
${y}^2+\left(a^{2}-2a-1\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(a^{3}-3a^{2}-a+3\right){x}^{2}-2a{x}-a^{3}+a^{2}+4a-5$ |
| 21.1-b2 |
21.1-b |
$2$ |
$3$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{9} \cdot 7^{3} \) |
$13.83461$ |
$(-a-1), (-a^3+2a^2+3a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3^{2} \) |
$0.043569511$ |
$231.7209466$ |
3.434785735 |
\( \frac{4664031550}{6751269} a^{3} - \frac{12967819862}{750141} a^{2} + \frac{59672832371}{6751269} a + \frac{29872652167}{6751269} \) |
\( \bigl[a^{3} - a^{2} - 5 a\) , \( -a^{3} + 2 a^{2} + 3 a - 2\) , \( a\) , \( -4 a^{3} + 3 a^{2} + 16 a + 6\) , \( -9 a^{3} + 13 a^{2} + 49 a + 11\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-2\right){x}^{2}+\left(-4a^{3}+3a^{2}+16a+6\right){x}-9a^{3}+13a^{2}+49a+11$ |
| 21.1-c1 |
21.1-c |
$2$ |
$3$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{9} \cdot 7^{3} \) |
$13.83461$ |
$(-a-1), (-a^3+2a^2+3a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.035058626$ |
$662.5415098$ |
2.634137240 |
\( \frac{4664031550}{6751269} a^{3} - \frac{12967819862}{750141} a^{2} + \frac{59672832371}{6751269} a + \frac{29872652167}{6751269} \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( -a^{2} + 2 a + 1\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( -5 a^{3} + 7 a^{2} + 23 a + 4\) , \( -47 a^{3} + 56 a^{2} + 232 a + 52\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(a^{3}-2a^{2}-3a+3\right){y}={x}^{3}+\left(-a^{2}+2a+1\right){x}^{2}+\left(-5a^{3}+7a^{2}+23a+4\right){x}-47a^{3}+56a^{2}+232a+52$ |
| 21.1-c2 |
21.1-c |
$2$ |
$3$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{3} \cdot 7 \) |
$13.83461$ |
$(-a-1), (-a^3+2a^2+3a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.105175879$ |
$662.5415098$ |
2.634137240 |
\( -\frac{80102}{189} a^{3} + \frac{24688}{21} a^{2} + \frac{201113}{189} a - \frac{284156}{189} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( -a^{3} + 2 a^{2} + 3 a - 1\) , \( 0\) , \( -a^{3} + 5 a^{2} + 6 a - 3\) , \( 2 a^{3} - a^{2} - 4 a + 5\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-1\right){x}^{2}+\left(-a^{3}+5a^{2}+6a-3\right){x}+2a^{3}-a^{2}-4a+5$ |
| 21.1-d1 |
21.1-d |
$6$ |
$8$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{16} \cdot 7^{8} \) |
$13.83461$ |
$(-a-1), (-a^3+2a^2+3a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$22.03183686$ |
1.665673418 |
\( -\frac{898589086686668844035}{248155780267521} a^{3} + \frac{163263946637405265181}{27572864474169} a^{2} + \frac{5263861833193040745233}{248155780267521} a + \frac{1266420698110974585316}{248155780267521} \) |
\( \bigl[a^{2} - 2 a - 1\) , \( -a^{3} + 2 a^{2} + 2 a - 1\) , \( a^{2} - 2 a - 1\) , \( 95 a^{3} - 187 a^{2} - 263 a - 57\) , \( 504 a^{3} - 568 a^{2} - 2550 a - 612\bigr] \) |
${y}^2+\left(a^{2}-2a-1\right){x}{y}+\left(a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-1\right){x}^{2}+\left(95a^{3}-187a^{2}-263a-57\right){x}+504a^{3}-568a^{2}-2550a-612$ |
| 21.1-d2 |
21.1-d |
$6$ |
$8$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{4} \cdot 7^{2} \) |
$13.83461$ |
$(-a-1), (-a^3+2a^2+3a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$352.5093898$ |
1.665673418 |
\( -\frac{85319533}{3969} a^{3} + \frac{20933642}{441} a^{2} + \frac{307507810}{3969} a - \frac{296298013}{3969} \) |
\( \bigl[a^{2} - 2 a - 1\) , \( -a^{3} + 2 a^{2} + 2 a - 1\) , \( a^{2} - 2 a - 1\) , \( 3 a^{2} - 8 a - 2\) , \( 3 a^{3} - 11 a^{2} + 5 a + 2\bigr] \) |
${y}^2+\left(a^{2}-2a-1\right){x}{y}+\left(a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-1\right){x}^{2}+\left(3a^{2}-8a-2\right){x}+3a^{3}-11a^{2}+5a+2$ |
| 21.1-d3 |
21.1-d |
$6$ |
$8$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{8} \cdot 7^{4} \) |
$13.83461$ |
$(-a-1), (-a^3+2a^2+3a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$88.12734747$ |
1.665673418 |
\( \frac{28918283118570229}{15752961} a^{3} - \frac{7254230548458608}{1750329} a^{2} - \frac{98850186870630073}{15752961} a + \frac{112226650825052689}{15752961} \) |
\( \bigl[a^{2} - 2 a - 1\) , \( -a^{3} + 2 a^{2} + 2 a - 1\) , \( a^{2} - 2 a - 1\) , \( 20 a^{3} - 62 a^{2} + 7 a + 3\) , \( 174 a^{3} - 595 a^{2} + 201 a + 93\bigr] \) |
${y}^2+\left(a^{2}-2a-1\right){x}{y}+\left(a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-1\right){x}^{2}+\left(20a^{3}-62a^{2}+7a+3\right){x}+174a^{3}-595a^{2}+201a+93$ |
| 21.1-d4 |
21.1-d |
$6$ |
$8$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{4} \cdot 7^{2} \) |
$13.83461$ |
$(-a-1), (-a^3+2a^2+3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{3} \) |
$1$ |
$5.507959217$ |
1.665673418 |
\( \frac{61454322416307957850243}{3969} a^{3} - \frac{15416010144890769909917}{441} a^{2} - \frac{210065945504149286427793}{3969} a + \frac{238492406894076670004716}{3969} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 2\) , \( a^{3} - 3 a^{2} + 4\) , \( a^{3} - a^{2} - 5 a\) , \( 24 a^{3} + 107 a^{2} + 32 a - 112\) , \( -1387 a^{3} - 843 a^{2} + 1913 a - 192\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+2\right){x}{y}+\left(a^{3}-a^{2}-5a\right){y}={x}^{3}+\left(a^{3}-3a^{2}+4\right){x}^{2}+\left(24a^{3}+107a^{2}+32a-112\right){x}-1387a^{3}-843a^{2}+1913a-192$ |
| 21.1-d5 |
21.1-d |
$6$ |
$8$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{8} \cdot 7^{16} \) |
$13.83461$ |
$(-a-1), (-a^3+2a^2+3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1$ |
$5.507959217$ |
1.665673418 |
\( -\frac{24324218882503346989897710983905}{218041257467152161} a^{3} + \frac{3130257293012684239299241034057}{24226806385239129} a^{2} + \frac{121012324553366544649411945327012}{218041257467152161} a + \frac{28895491954981087218640032315401}{218041257467152161} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 2\) , \( a^{3} - 3 a^{2} + 4\) , \( a^{3} - a^{2} - 5 a\) , \( -291 a^{3} - 473 a^{2} - 28 a + 13\) , \( -19232 a^{3} - 20526 a^{2} + 18175 a + 5705\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+2\right){x}{y}+\left(a^{3}-a^{2}-5a\right){y}={x}^{3}+\left(a^{3}-3a^{2}+4\right){x}^{2}+\left(-291a^{3}-473a^{2}-28a+13\right){x}-19232a^{3}-20526a^{2}+18175a+5705$ |
| 21.1-d6 |
21.1-d |
$6$ |
$8$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{32} \cdot 7^{4} \) |
$13.83461$ |
$(-a-1), (-a^3+2a^2+3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{7} \) |
$1$ |
$1.376989804$ |
1.665673418 |
\( \frac{93351032504292897897277178575777}{4449101473433270241} a^{3} + \frac{10048303108249112395936794750967}{494344608159252249} a^{2} - \frac{104925144694088217346797735597220}{4449101473433270241} a - \frac{31444454475335045120254874254073}{4449101473433270241} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 3\) , \( a^{2} - a - 1\) , \( a + 1\) , \( 56 a^{3} + 34 a^{2} - 483 a - 322\) , \( -3930 a^{3} + 10492 a^{2} + 10882 a - 21942\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(56a^{3}+34a^{2}-483a-322\right){x}-3930a^{3}+10492a^{2}+10882a-21942$ |
| 33.2-a1 |
33.2-a |
$4$ |
$6$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
33.2 |
\( 3 \cdot 11 \) |
\( 3 \cdot 11^{3} \) |
$14.63874$ |
$(-a-1), (-a^3+a^2+6a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$386.0266600$ |
2.736073271 |
\( -\frac{2720692}{3993} a^{3} + \frac{1426603}{1331} a^{2} + \frac{9446497}{3993} a + \frac{2098835}{3993} \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( a^{3} - 3 a^{2} - a + 3\) , \( a\) , \( -2 a^{3} + 2 a^{2} + 2 a + 4\) , \( -6 a^{3} - 9 a^{2} + 9 a + 4\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-3a^{2}-a+3\right){x}^{2}+\left(-2a^{3}+2a^{2}+2a+4\right){x}-6a^{3}-9a^{2}+9a+4$ |
| 33.2-a2 |
33.2-a |
$4$ |
$6$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
33.2 |
\( 3 \cdot 11 \) |
\( 3^{2} \cdot 11^{6} \) |
$14.63874$ |
$(-a-1), (-a^3+a^2+6a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$96.50666500$ |
2.736073271 |
\( \frac{47638230136}{15944049} a^{3} + \frac{538972678677}{1771561} a^{2} - \frac{3519943051375}{15944049} a + \frac{18627664474}{15944049} \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( a^{3} - 3 a^{2} - a + 3\) , \( a\) , \( -22 a^{3} - 18 a^{2} + 27 a + 9\) , \( -259 a^{3} - 249 a^{2} + 294 a + 85\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-3a^{2}-a+3\right){x}^{2}+\left(-22a^{3}-18a^{2}+27a+9\right){x}-259a^{3}-249a^{2}+294a+85$ |
| 33.2-a3 |
33.2-a |
$4$ |
$6$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
33.2 |
\( 3 \cdot 11 \) |
\( 3^{6} \cdot 11^{2} \) |
$14.63874$ |
$(-a-1), (-a^3+a^2+6a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$96.50666500$ |
2.736073271 |
\( -\frac{7612866580234163451776}{88209} a^{3} + \frac{3005290119175586899765}{9801} a^{2} - \frac{11550262271625687801811}{88209} a - \frac{4902413812698686818199}{88209} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - a^{2} - 4 a - 1\) , \( a^{3} - 2 a^{2} - 2 a + 2\) , \( 25 a^{3} - 45 a^{2} - 54 a - 38\) , \( -24 a^{3} - 99 a^{2} + 487 a + 171\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{3}-2a^{2}-2a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a-1\right){x}^{2}+\left(25a^{3}-45a^{2}-54a-38\right){x}-24a^{3}-99a^{2}+487a+171$ |
| 33.2-a4 |
33.2-a |
$4$ |
$6$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
33.2 |
\( 3 \cdot 11 \) |
\( 3^{3} \cdot 11 \) |
$14.63874$ |
$(-a-1), (-a^3+a^2+6a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$386.0266600$ |
2.736073271 |
\( -\frac{462746900380}{297} a^{3} + \frac{65749641671}{33} a^{2} + \frac{2150893298167}{297} a + \frac{507030397112}{297} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - a^{2} - 4 a - 1\) , \( a^{3} - 2 a^{2} - 2 a + 2\) , \( 20 a^{3} - 20 a^{2} - 89 a - 23\) , \( -84 a^{3} + 103 a^{2} + 439 a + 106\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{3}-2a^{2}-2a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a-1\right){x}^{2}+\left(20a^{3}-20a^{2}-89a-23\right){x}-84a^{3}+103a^{2}+439a+106$ |
| 33.2-b1 |
33.2-b |
$4$ |
$10$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
33.2 |
\( 3 \cdot 11 \) |
\( 3^{2} \cdot 11^{10} \) |
$14.63874$ |
$(-a-1), (-a^3+a^2+6a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$25$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$1.334138612$ |
1.576014204 |
\( \frac{5010848879145922415898072883}{233436821409} a^{3} - \frac{1256987093509642228236874403}{25937424601} a^{2} - \frac{17128309670905468419722265079}{233436821409} a + \frac{19446139539506924666962856671}{233436821409} \) |
\( \bigl[a^{3} - a^{2} - 5 a\) , \( a^{3} - 2 a^{2} - 2 a + 2\) , \( 1\) , \( -1110 a^{3} - 593 a^{2} + 1644 a - 302\) , \( -67294 a^{3} - 59338 a^{2} + 79981 a + 14846\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a\right){x}{y}+{y}={x}^{3}+\left(a^{3}-2a^{2}-2a+2\right){x}^{2}+\left(-1110a^{3}-593a^{2}+1644a-302\right){x}-67294a^{3}-59338a^{2}+79981a+14846$ |
| 33.2-b2 |
33.2-b |
$4$ |
$10$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
33.2 |
\( 3 \cdot 11 \) |
\( 3 \cdot 11^{5} \) |
$14.63874$ |
$(-a-1), (-a^3+a^2+6a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$100$ |
\( 5 \) |
$1$ |
$1.334138612$ |
1.576014204 |
\( -\frac{5884869327490246761505}{483153} a^{3} + \frac{6969413984757758197102}{161051} a^{2} - \frac{8928539876882610463355}{483153} a - \frac{3789645485338071113602}{483153} \) |
\( \bigl[a^{3} - a^{2} - 5 a\) , \( a^{3} - 2 a^{2} - 2 a + 2\) , \( 1\) , \( -60 a^{3} - 68 a^{2} + 114 a - 12\) , \( -1118 a^{3} - 1119 a^{2} + 1412 a + 254\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a\right){x}{y}+{y}={x}^{3}+\left(a^{3}-2a^{2}-2a+2\right){x}^{2}+\left(-60a^{3}-68a^{2}+114a-12\right){x}-1118a^{3}-1119a^{2}+1412a+254$ |
| 33.2-b3 |
33.2-b |
$4$ |
$10$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
33.2 |
\( 3 \cdot 11 \) |
\( 3^{5} \cdot 11 \) |
$14.63874$ |
$(-a-1), (-a^3+a^2+6a)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$4$ |
\( 5 \) |
$1$ |
$833.8366328$ |
1.576014204 |
\( -\frac{59717107}{2673} a^{3} + \frac{7822289}{297} a^{2} + \frac{293595790}{2673} a + \frac{72188672}{2673} \) |
\( \bigl[a^{3} - a^{2} - 5 a\) , \( a^{3} - 2 a^{2} - 2 a + 2\) , \( 1\) , \( 2 a^{2} + 4 a + 3\) , \( 3 a^{3} + 3 a^{2} - 2 a\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a\right){x}{y}+{y}={x}^{3}+\left(a^{3}-2a^{2}-2a+2\right){x}^{2}+\left(2a^{2}+4a+3\right){x}+3a^{3}+3a^{2}-2a$ |
| 33.2-b4 |
33.2-b |
$4$ |
$10$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
33.2 |
\( 3 \cdot 11 \) |
\( 3^{10} \cdot 11^{2} \) |
$14.63874$ |
$(-a-1), (-a^3+a^2+6a)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$833.8366328$ |
1.576014204 |
\( -\frac{19636369736226863}{7144929} a^{3} + \frac{2526985602376480}{793881} a^{2} + \frac{97690343057904548}{7144929} a + \frac{23326657782587476}{7144929} \) |
\( \bigl[a^{3} - a^{2} - 5 a\) , \( a^{3} - 2 a^{2} - 2 a + 2\) , \( 1\) , \( -5 a^{3} - 3 a^{2} + 9 a + 3\) , \( 6 a^{3} + 7 a^{2} - 6 a - 3\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a\right){x}{y}+{y}={x}^{3}+\left(a^{3}-2a^{2}-2a+2\right){x}^{2}+\left(-5a^{3}-3a^{2}+9a+3\right){x}+6a^{3}+7a^{2}-6a-3$ |
| 33.2-c1 |
33.2-c |
$4$ |
$10$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
33.2 |
\( 3 \cdot 11 \) |
\( 3^{2} \cdot 11^{10} \) |
$14.63874$ |
$(-a-1), (-a^3+a^2+6a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.641646935$ |
$26.23536348$ |
3.181722993 |
\( \frac{5010848879145922415898072883}{233436821409} a^{3} - \frac{1256987093509642228236874403}{25937424601} a^{2} - \frac{17128309670905468419722265079}{233436821409} a + \frac{19446139539506924666962856671}{233436821409} \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( a^{2} - 2 a - 2\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( 346 a^{3} - 1401 a^{2} + 1080 a - 151\) , \( -12866 a^{3} + 46772 a^{2} - 24605 a - 4803\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(a^{3}-2a^{2}-3a+3\right){y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(346a^{3}-1401a^{2}+1080a-151\right){x}-12866a^{3}+46772a^{2}-24605a-4803$ |
| 33.2-c2 |
33.2-c |
$4$ |
$10$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
33.2 |
\( 3 \cdot 11 \) |
\( 3^{10} \cdot 11^{2} \) |
$14.63874$ |
$(-a-1), (-a^3+a^2+6a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$0.128329387$ |
$655.8840872$ |
3.181722993 |
\( -\frac{19636369736226863}{7144929} a^{3} + \frac{2526985602376480}{793881} a^{2} + \frac{97690343057904548}{7144929} a + \frac{23326657782587476}{7144929} \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( a^{2} - 2 a - 2\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( 6 a^{3} - 16 a^{2} - 1\) , \( 18 a^{3} - 66 a^{2} + 39 a + 12\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(a^{3}-2a^{2}-3a+3\right){y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(6a^{3}-16a^{2}-1\right){x}+18a^{3}-66a^{2}+39a+12$ |
| 33.2-c3 |
33.2-c |
$4$ |
$10$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
33.2 |
\( 3 \cdot 11 \) |
\( 3^{5} \cdot 11 \) |
$14.63874$ |
$(-a-1), (-a^3+a^2+6a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 1 \) |
$0.256658774$ |
$1311.768174$ |
3.181722993 |
\( -\frac{59717107}{2673} a^{3} + \frac{7822289}{297} a^{2} + \frac{293595790}{2673} a + \frac{72188672}{2673} \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( a^{2} - 2 a - 2\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( a^{3} - a^{2} - 1\) , \( 2 a^{2} + 2 a - 3\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(a^{3}-2a^{2}-3a+3\right){y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(a^{3}-a^{2}-1\right){x}+2a^{2}+2a-3$ |
| 33.2-c4 |
33.2-c |
$4$ |
$10$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
33.2 |
\( 3 \cdot 11 \) |
\( 3 \cdot 11^{5} \) |
$14.63874$ |
$(-a-1), (-a^3+a^2+6a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 5 \) |
$1.283293870$ |
$52.47072697$ |
3.181722993 |
\( -\frac{5884869327490246761505}{483153} a^{3} + \frac{6969413984757758197102}{161051} a^{2} - \frac{8928539876882610463355}{483153} a - \frac{3789645485338071113602}{483153} \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( a^{2} - 2 a - 2\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( 461 a^{3} - 1636 a^{2} + 705 a + 264\) , \( -13834 a^{3} + 49189 a^{2} - 21134 a - 8866\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(a^{3}-2a^{2}-3a+3\right){y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(461a^{3}-1636a^{2}+705a+264\right){x}-13834a^{3}+49189a^{2}-21134a-8866$ |
| 33.2-d1 |
33.2-d |
$4$ |
$6$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
33.2 |
\( 3 \cdot 11 \) |
\( 3 \cdot 11^{3} \) |
$14.63874$ |
$(-a-1), (-a^3+a^2+6a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$0.134166328$ |
$763.8927637$ |
2.905670383 |
\( -\frac{2720692}{3993} a^{3} + \frac{1426603}{1331} a^{2} + \frac{9446497}{3993} a + \frac{2098835}{3993} \) |
\( \bigl[a\) , \( a^{3} - a^{2} - 6 a\) , \( a^{3} - a^{2} - 4 a\) , \( -5 a^{2} + 11 a + 4\) , \( 2 a^{3} - 5 a^{2} - 5 a - 1\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-a^{2}-4a\right){y}={x}^{3}+\left(a^{3}-a^{2}-6a\right){x}^{2}+\left(-5a^{2}+11a+4\right){x}+2a^{3}-5a^{2}-5a-1$ |
| 33.2-d2 |
33.2-d |
$4$ |
$6$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
33.2 |
\( 3 \cdot 11 \) |
\( 3^{2} \cdot 11^{6} \) |
$14.63874$ |
$(-a-1), (-a^3+a^2+6a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.067083164$ |
$381.9463818$ |
2.905670383 |
\( \frac{47638230136}{15944049} a^{3} + \frac{538972678677}{1771561} a^{2} - \frac{3519943051375}{15944049} a + \frac{18627664474}{15944049} \) |
\( \bigl[a\) , \( a^{3} - a^{2} - 6 a\) , \( a^{3} - a^{2} - 4 a\) , \( 25 a^{3} - 95 a^{2} + 51 a + 19\) , \( -174 a^{3} + 619 a^{2} - 271 a - 114\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-a^{2}-4a\right){y}={x}^{3}+\left(a^{3}-a^{2}-6a\right){x}^{2}+\left(25a^{3}-95a^{2}+51a+19\right){x}-174a^{3}+619a^{2}-271a-114$ |
| 33.2-d3 |
33.2-d |
$4$ |
$6$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
33.2 |
\( 3 \cdot 11 \) |
\( 3^{6} \cdot 11^{2} \) |
$14.63874$ |
$(-a-1), (-a^3+a^2+6a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.201249492$ |
$381.9463818$ |
2.905670383 |
\( -\frac{7612866580234163451776}{88209} a^{3} + \frac{3005290119175586899765}{9801} a^{2} - \frac{11550262271625687801811}{88209} a - \frac{4902413812698686818199}{88209} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 2\) , \( -a^{3} + 2 a^{2} + 4 a - 1\) , \( a^{2} - 2 a - 1\) , \( -5 a^{3} + 13 a^{2} + 2 a - 36\) , \( -22 a^{3} + 43 a^{2} + 86 a - 57\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+2\right){x}{y}+\left(a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-1\right){x}^{2}+\left(-5a^{3}+13a^{2}+2a-36\right){x}-22a^{3}+43a^{2}+86a-57$ |
| 33.2-d4 |
33.2-d |
$4$ |
$6$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
33.2 |
\( 3 \cdot 11 \) |
\( 3^{3} \cdot 11 \) |
$14.63874$ |
$(-a-1), (-a^3+a^2+6a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.402498985$ |
$763.8927637$ |
2.905670383 |
\( -\frac{462746900380}{297} a^{3} + \frac{65749641671}{33} a^{2} + \frac{2150893298167}{297} a + \frac{507030397112}{297} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 2\) , \( -a^{3} + 2 a^{2} + 4 a - 1\) , \( a^{2} - 2 a - 1\) , \( 5 a^{3} - 2 a^{2} - 28 a - 6\) , \( -5 a^{3} + 10 a^{2} + 31 a + 3\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+2\right){x}{y}+\left(a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-1\right){x}^{2}+\left(5a^{3}-2a^{2}-28a-6\right){x}-5a^{3}+10a^{2}+31a+3$ |
| 39.1-a1 |
39.1-a |
$2$ |
$2$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( 3^{16} \cdot 13^{4} \) |
$14.94763$ |
$(-a-1), (a^2-2a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.199463272$ |
$187.2367573$ |
2.823535146 |
\( -\frac{801752857236854408}{1229457398481} a^{3} + \frac{319088858345844448}{136606377609} a^{2} - \frac{1305500676828935869}{1229457398481} a - \frac{457087746523336856}{1229457398481} \) |
\( \bigl[a^{2} - 2 a - 1\) , \( a^{3} - 2 a^{2} - 3 a + 1\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( -a^{3} - a^{2} + 3 a + 1\) , \( 4 a^{3} + 7 a^{2} - 3 a - 4\bigr] \) |
${y}^2+\left(a^{2}-2a-1\right){x}{y}+\left(a^{3}-2a^{2}-3a+2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+1\right){x}^{2}+\left(-a^{3}-a^{2}+3a+1\right){x}+4a^{3}+7a^{2}-3a-4$ |
| 39.1-a2 |
39.1-a |
$2$ |
$2$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( 3^{8} \cdot 13^{2} \) |
$14.94763$ |
$(-a-1), (a^2-2a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.099731636$ |
$748.9470294$ |
2.823535146 |
\( \frac{13276665632}{1108809} a^{3} + \frac{1541289641}{123201} a^{2} - \frac{11060755568}{1108809} a - \frac{3544330384}{1108809} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 3\) , \( -a^{3} + a^{2} + 6 a\) , \( a^{3} - a^{2} - 4 a\) , \( -2 a^{3} + 3 a^{2} + 7 a - 1\) , \( -18 a^{3} + 40 a^{2} + 61 a - 70\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+3\right){x}{y}+\left(a^{3}-a^{2}-4a\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a\right){x}^{2}+\left(-2a^{3}+3a^{2}+7a-1\right){x}-18a^{3}+40a^{2}+61a-70$ |
| 39.1-b1 |
39.1-b |
$1$ |
$1$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( 3 \cdot 13 \) |
$14.94763$ |
$(-a-1), (a^2-2a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1.479965926$ |
$50.52075570$ |
2.826381014 |
\( \frac{1568037508964}{39} a^{3} - \frac{1857017012602}{13} a^{2} + \frac{2379030713467}{39} a + \frac{1009760062646}{39} \) |
\( \bigl[a^{2} - a - 2\) , \( a\) , \( a^{3} - a^{2} - 4 a\) , \( 5 a^{3} - 8 a^{2} - 20 a + 7\) , \( 9 a^{3} - 14 a^{2} - 37 a + 10\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{3}-a^{2}-4a\right){y}={x}^{3}+a{x}^{2}+\left(5a^{3}-8a^{2}-20a+7\right){x}+9a^{3}-14a^{2}-37a+10$ |
| 39.1-c1 |
39.1-c |
$2$ |
$2$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( 3^{8} \cdot 13^{2} \) |
$14.94763$ |
$(-a-1), (a^2-2a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.057376925$ |
$518.7485922$ |
4.500526763 |
\( \frac{13276665632}{1108809} a^{3} + \frac{1541289641}{123201} a^{2} - \frac{11060755568}{1108809} a - \frac{3544330384}{1108809} \) |
\( \bigl[a^{2} - 2 a - 2\) , \( a^{2} - 3 a - 1\) , \( a\) , \( -a^{3} + 6 a^{2} - 8 a - 4\) , \( 8 a^{3} - 19 a^{2} - 29 a + 42\bigr] \) |
${y}^2+\left(a^{2}-2a-2\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-3a-1\right){x}^{2}+\left(-a^{3}+6a^{2}-8a-4\right){x}+8a^{3}-19a^{2}-29a+42$ |
| 39.1-c2 |
39.1-c |
$2$ |
$2$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( 3^{16} \cdot 13^{4} \) |
$14.94763$ |
$(-a-1), (a^2-2a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.114753851$ |
$129.6871480$ |
4.500526763 |
\( -\frac{801752857236854408}{1229457398481} a^{3} + \frac{319088858345844448}{136606377609} a^{2} - \frac{1305500676828935869}{1229457398481} a - \frac{457087746523336856}{1229457398481} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 2\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a^{2} - 2 a - 2\) , \( 29 a^{3} - 100 a^{2} + 48 a + 24\) , \( 270 a^{3} - 953 a^{2} + 411 a + 174\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+2\right){x}{y}+\left(a^{2}-2a-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+1\right){x}^{2}+\left(29a^{3}-100a^{2}+48a+24\right){x}+270a^{3}-953a^{2}+411a+174$ |
| 39.1-d1 |
39.1-d |
$1$ |
$1$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( 3 \cdot 13 \) |
$14.94763$ |
$(-a-1), (a^2-2a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.345083358$ |
$338.7195635$ |
4.418485652 |
\( \frac{1568037508964}{39} a^{3} - \frac{1857017012602}{13} a^{2} + \frac{2379030713467}{39} a + \frac{1009760062646}{39} \) |
\( \bigl[1\) , \( -a^{3} + 2 a^{2} + 3 a - 3\) , \( a^{3} - a^{2} - 4 a + 1\) , \( 8 a^{3} - 12 a^{2} - 36 a + 2\) , \( 14 a^{3} - 12 a^{2} - 78 a - 40\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-3\right){x}^{2}+\left(8a^{3}-12a^{2}-36a+2\right){x}+14a^{3}-12a^{2}-78a-40$ |
| 48.1-a1 |
48.1-a |
$1$ |
$1$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{4} \cdot 3^{8} \) |
$15.34068$ |
$(-a-1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$80.47450331$ |
1.521028884 |
\( \frac{283554753371}{13122} a^{3} - \frac{18244263680}{729} a^{2} - \frac{705346823302}{6561} a - \frac{168459117986}{6561} \) |
\( \bigl[a\) , \( a^{3} - a^{2} - 6 a\) , \( a^{3} - a^{2} - 5 a + 1\) , \( 10 a^{3} - 40 a^{2} + 26 a + 10\) , \( 129 a^{3} - 456 a^{2} + 189 a + 80\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-a^{2}-5a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-6a\right){x}^{2}+\left(10a^{3}-40a^{2}+26a+10\right){x}+129a^{3}-456a^{2}+189a+80$ |
| 48.1-b1 |
48.1-b |
$2$ |
$3$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{12} \cdot 3^{6} \) |
$15.34068$ |
$(-a-1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$53.30391404$ |
1.007484229 |
\( -\frac{1584500055649}{5832} a^{3} + \frac{99369151829}{162} a^{2} + \frac{677026685375}{729} a - \frac{1537283329873}{1458} \) |
\( \bigl[a^{2} - 2 a - 2\) , \( -a^{3} + 3 a^{2} + 2 a - 4\) , \( a^{2} - a - 2\) , \( -9 a^{3} + 22 a^{2} + 26 a - 34\) , \( -13 a^{3} + 30 a^{2} + 40 a - 48\bigr] \) |
${y}^2+\left(a^{2}-2a-2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+2a-4\right){x}^{2}+\left(-9a^{3}+22a^{2}+26a-34\right){x}-13a^{3}+30a^{2}+40a-48$ |
| 48.1-b2 |
48.1-b |
$2$ |
$3$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{4} \cdot 3^{2} \) |
$15.34068$ |
$(-a-1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$53.30391404$ |
1.007484229 |
\( -\frac{782719}{18} a^{3} - \frac{111335}{2} a^{2} + \frac{212216}{9} a + \frac{76774}{9} \) |
\( \bigl[a^{3} - a^{2} - 5 a\) , \( a^{3} - 3 a^{2} - 2 a + 4\) , \( 0\) , \( 2 a^{3} - 2 a^{2} - 13 a + 4\) , \( 12 a^{3} - 19 a^{2} - 47 a - 7\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a\right){x}{y}={x}^{3}+\left(a^{3}-3a^{2}-2a+4\right){x}^{2}+\left(2a^{3}-2a^{2}-13a+4\right){x}+12a^{3}-19a^{2}-47a-7$ |
| 48.1-c1 |
48.1-c |
$1$ |
$1$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{4} \cdot 3^{8} \) |
$15.34068$ |
$(-a-1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$0.242919902$ |
$66.57161144$ |
4.890477964 |
\( \frac{283554753371}{13122} a^{3} - \frac{18244263680}{729} a^{2} - \frac{705346823302}{6561} a - \frac{168459117986}{6561} \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( a^{3} - 3 a^{2} - a + 3\) , \( 1\) , \( a^{3} + 5 a^{2} + 2\) , \( 6 a^{3} + 7 a^{2} - 6 a - 2\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+{y}={x}^{3}+\left(a^{3}-3a^{2}-a+3\right){x}^{2}+\left(a^{3}+5a^{2}+2\right){x}+6a^{3}+7a^{2}-6a-2$ |
| 48.1-d1 |
48.1-d |
$2$ |
$3$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{4} \cdot 3^{2} \) |
$15.34068$ |
$(-a-1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.396507490$ |
$156.5973069$ |
4.694343153 |
\( -\frac{782719}{18} a^{3} - \frac{111335}{2} a^{2} + \frac{212216}{9} a + \frac{76774}{9} \) |
\( \bigl[a\) , \( a^{3} - 3 a^{2} - 2 a + 5\) , \( a^{2} - 2 a - 1\) , \( 2 a^{3} - 4 a^{2} - 10 a + 7\) , \( 3 a^{3} - 6 a^{2} - 11 a + 3\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-2a-1\right){y}={x}^{3}+\left(a^{3}-3a^{2}-2a+5\right){x}^{2}+\left(2a^{3}-4a^{2}-10a+7\right){x}+3a^{3}-6a^{2}-11a+3$ |
| 48.1-d2 |
48.1-d |
$2$ |
$3$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{12} \cdot 3^{6} \) |
$15.34068$ |
$(-a-1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$0.132169163$ |
$156.5973069$ |
4.694343153 |
\( -\frac{1584500055649}{5832} a^{3} + \frac{99369151829}{162} a^{2} + \frac{677026685375}{729} a - \frac{1537283329873}{1458} \) |
\( \bigl[a^{3} - a^{2} - 5 a + 1\) , \( a^{3} - 2 a^{2} - 2 a + 1\) , \( a^{3} - 2 a^{2} - 2 a + 2\) , \( -6 a^{3} + 13 a^{2} + 25 a - 25\) , \( 11 a^{3} - 28 a^{2} - 23 a + 33\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a+1\right){x}{y}+\left(a^{3}-2a^{2}-2a+2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-2a+1\right){x}^{2}+\left(-6a^{3}+13a^{2}+25a-25\right){x}+11a^{3}-28a^{2}-23a+33$ |
| 49.1-a1 |
49.1-a |
$2$ |
$2$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{6} \) |
$15.38027$ |
$(-a^3+2a^2+3a-1)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3Ns |
|
\( 2^{2} \) |
$1$ |
$32.48139345$ |
5.465296849 |
\( -285016019 a^{3} + 1173815244 a^{2} - 586612960 a - 167968054 \) |
\( \bigl[a^{2} - a - 2\) , \( a^{3} - a^{2} - 6 a + 1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( 21 a^{3} - 76 a^{2} + 32 a + 18\) , \( -470 a^{3} + 113 a^{2} + 3505 a + 887\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-6a+1\right){x}^{2}+\left(21a^{3}-76a^{2}+32a+18\right){x}-470a^{3}+113a^{2}+3505a+887$ |
| 49.1-a2 |
49.1-a |
$2$ |
$2$ |
4.4.11197.1 |
$4$ |
$[4, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{6} \) |
$15.38027$ |
$(-a^3+2a^2+3a-1)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3Ns |
|
\( 2 \) |
$1$ |
$129.9255738$ |
5.465296849 |
\( -5135 a^{3} - 1591 a^{2} + 58206 a + 7612 \) |
\( \bigl[a^{2} - 2 a - 1\) , \( a^{3} - 2 a^{2} - 4 a + 3\) , \( a\) , \( 5 a^{3} - 23 a^{2} + 26 a - 8\) , \( 48 a^{3} - 190 a^{2} + 146 a - 17\bigr] \) |
${y}^2+\left(a^{2}-2a-1\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-2a^{2}-4a+3\right){x}^{2}+\left(5a^{3}-23a^{2}+26a-8\right){x}+48a^{3}-190a^{2}+146a-17$ |
*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.
