| 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 |
| 8.1-a1 |
8.1-a |
$1$ |
$1$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{6} \) |
$5.39865$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$25.34154389$ |
1.186401347 |
\( -25221 a^{2} - \frac{569429}{4} a - \frac{811355}{4} \) |
\( \bigl[a + 1\) , \( a^{2} - 5\) , \( a\) , \( a + 2\) , \( -a^{2} - 2 a + 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(a+2\right){x}-a^{2}-2a+1$ |
| 8.1-b1 |
8.1-b |
$4$ |
$15$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{45} \) |
$5.39865$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3, 5$ |
3B, 5B.4.1 |
$1$ |
\( 1 \) |
$3.974254708$ |
$11.37605449$ |
3.174952128 |
\( \frac{46969655}{32768} \) |
\( \bigl[a^{2} + a - 5\) , \( a^{2} + a - 5\) , \( a + 1\) , \( 345 a^{2} + 664 a - 822\) , \( -1815 a^{2} - 3483 a + 4352\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(345a^{2}+664a-822\right){x}-1815a^{2}-3483a+4352$ |
| 8.1-b2 |
8.1-b |
$4$ |
$15$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{15} \) |
$5.39865$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3, 5$ |
3B, 5B.4.1 |
$1$ |
\( 1 \) |
$1.324751569$ |
$34.12816347$ |
3.174952128 |
\( -\frac{121945}{32} \) |
\( \bigl[a^{2} + a - 5\) , \( a^{2} + a - 5\) , \( a + 1\) , \( -40 a^{2} - 76 a + 98\) , \( 259 a^{2} + 497 a - 622\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(-40a^{2}-76a+98\right){x}+259a^{2}+497a-622$ |
| 8.1-b3 |
8.1-b |
$4$ |
$15$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{3} \) |
$5.39865$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3, 5$ |
3B, 5B.4.2 |
$1$ |
\( 1 \) |
$0.264950313$ |
$170.6408173$ |
3.174952128 |
\( -\frac{25}{2} \) |
\( \bigl[a + 1\) , \( a^{2} - a - 7\) , \( a^{2} + a - 5\) , \( -3 a^{2} - 3 a + 21\) , \( -a^{2} - 6 a - 6\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(a^{2}-a-7\right){x}^{2}+\left(-3a^{2}-3a+21\right){x}-a^{2}-6a-6$ |
| 8.1-b4 |
8.1-b |
$4$ |
$15$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{9} \) |
$5.39865$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3, 5$ |
3B, 5B.4.2 |
$1$ |
\( 1 \) |
$0.794850941$ |
$56.88027246$ |
3.174952128 |
\( -\frac{349938025}{8} \) |
\( \bigl[a + 1\) , \( a^{2} - a - 7\) , \( a^{2} + a - 5\) , \( -58 a^{2} - 108 a + 151\) , \( -586 a^{2} - 1127 a + 1399\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(a^{2}-a-7\right){x}^{2}+\left(-58a^{2}-108a+151\right){x}-586a^{2}-1127a+1399$ |
| 8.1-c1 |
8.1-c |
$4$ |
$15$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{9} \) |
$5.39865$ |
$(2)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3B.1.2, 5B.1.3 |
|
\( 1 \) |
$1$ |
$1.813593847$ |
3.181351283 |
\( -\frac{349938025}{8} \) |
\( \bigl[a^{2} + a - 6\) , \( 0\) , \( a^{2} + a - 5\) , \( -5 a^{2} - 30 a - 45\) , \( -64 a^{2} - 224 a - 128\bigr] \) |
${y}^2+\left(a^{2}+a-6\right){x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(-5a^{2}-30a-45\right){x}-64a^{2}-224a-128$ |
| 8.1-c2 |
8.1-c |
$4$ |
$15$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{3} \) |
$5.39865$ |
$(2)$ |
$0 \le r \le 1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3B.1.1, 5B.1.3 |
|
\( 1 \) |
$1$ |
$48.96703389$ |
3.181351283 |
\( -\frac{25}{2} \) |
\( \bigl[a^{2} + a - 6\) , \( 0\) , \( a^{2} + a - 5\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}+a-6\right){x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}$ |
| 8.1-c3 |
8.1-c |
$4$ |
$15$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{45} \) |
$5.39865$ |
$(2)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3B.1.2, 5B.1.4 |
|
\( 1 \) |
$1$ |
$9.067969238$ |
3.181351283 |
\( \frac{46969655}{32768} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 67 a^{2} + 181 a - 11\) , \( -293 a^{2} - 680 a + 374\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(67a^{2}+181a-11\right){x}-293a^{2}-680a+374$ |
| 8.1-c4 |
8.1-c |
$4$ |
$15$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{15} \) |
$5.39865$ |
$(2)$ |
$0 \le r \le 1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3B.1.1, 5B.1.4 |
|
\( 1 \) |
$1$ |
$244.8351694$ |
3.181351283 |
\( -\frac{121945}{32} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -8 a^{2} - 24 a - 1\) , \( 40 a^{2} + 93 a - 52\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-8a^{2}-24a-1\right){x}+40a^{2}+93a-52$ |
| 8.1-d1 |
8.1-d |
$1$ |
$1$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{6} \) |
$5.39865$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$40.94866624$ |
1.917071549 |
\( -25221 a^{2} - \frac{569429}{4} a - \frac{811355}{4} \) |
\( \bigl[a^{2} + a - 6\) , \( 1\) , \( a + 1\) , \( 2 a + 5\) , \( a^{2} + 2 a - 3\bigr] \) |
${y}^2+\left(a^{2}+a-6\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(2a+5\right){x}+a^{2}+2a-3$ |
| 27.1-a1 |
27.1-a |
$2$ |
$5$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{3} \) |
$6.61197$ |
$(3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 1 \) |
$0.356266079$ |
$152.9086637$ |
3.825572072 |
\( -\frac{102400}{3} \) |
\( \bigl[0\) , \( a^{2} - a - 6\) , \( a\) , \( -5 a^{2} - 8 a + 23\) , \( -8 a^{2} - 18 a + 13\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(-5a^{2}-8a+23\right){x}-8a^{2}-18a+13$ |
| 27.1-a2 |
27.1-a |
$2$ |
$5$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{15} \) |
$6.61197$ |
$(3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$1.781330399$ |
$30.58173274$ |
3.825572072 |
\( \frac{20480}{243} \) |
\( \bigl[0\) , \( a + 1\) , \( a + 1\) , \( 26 a^{2} + 50 a - 61\) , \( 792 a^{2} + 1520 a - 1900\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(26a^{2}+50a-61\right){x}+792a^{2}+1520a-1900$ |
| 27.1-b1 |
27.1-b |
$2$ |
$5$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{3} \) |
$6.61197$ |
$(3)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.3 |
|
\( 1 \) |
$1$ |
$13.79480980$ |
3.559779693 |
\( -\frac{102400}{3} \) |
\( \bigl[0\) , \( a\) , \( a^{2} + a - 5\) , \( -2 a - 3\) , \( -2 a^{2} - 6 a - 2\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){y}={x}^{3}+a{x}^{2}+\left(-2a-3\right){x}-2a^{2}-6a-2$ |
| 27.1-b2 |
27.1-b |
$2$ |
$5$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{15} \) |
$6.61197$ |
$(3)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.4 |
|
\( 1 \) |
$1$ |
$68.97404900$ |
3.559779693 |
\( \frac{20480}{243} \) |
\( \bigl[0\) , \( -a^{2} + 6\) , \( a\) , \( 4 a^{2} + 14 a + 9\) , \( 84 a^{2} + 197 a - 104\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(4a^{2}+14a+9\right){x}+84a^{2}+197a-104$ |
| 31.1-a1 |
31.1-a |
$1$ |
$1$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
31.1 |
\( 31 \) |
\( -31 \) |
$6.76597$ |
$(a^2-10)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.959575459$ |
$66.24420773$ |
4.463924733 |
\( -\frac{26320131}{31} a^{2} - \frac{50567719}{31} a + \frac{62942284}{31} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -5 a^{2} - 11 a + 12\) , \( 21 a^{2} + 40 a - 51\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-5a^{2}-11a+12\right){x}+21a^{2}+40a-51$ |
| 31.1-b1 |
31.1-b |
$1$ |
$1$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
31.1 |
\( 31 \) |
\( -31 \) |
$6.76597$ |
$(a^2-10)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.089646928$ |
$419.5870474$ |
2.641479896 |
\( -\frac{26320131}{31} a^{2} - \frac{50567719}{31} a + \frac{62942284}{31} \) |
\( \bigl[a^{2} + a - 6\) , \( -a^{2} + 5\) , \( a\) , \( -24 a^{2} - 38 a + 80\) , \( 87 a^{2} + 175 a - 188\bigr] \) |
${y}^2+\left(a^{2}+a-6\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-24a^{2}-38a+80\right){x}+87a^{2}+175a-188$ |
| 35.1-a1 |
35.1-a |
$4$ |
$6$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5^{3} \cdot 7^{12} \) |
$6.90422$ |
$(a-2), (-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$4.697805787$ |
$24.42639829$ |
4.029158180 |
\( -\frac{5523209449580259866763}{69206436005} a^{2} + \frac{761127012824843830457}{69206436005} a + \frac{44841915529379799234402}{69206436005} \) |
\( \bigl[a\) , \( a + 1\) , \( a^{2} - 6\) , \( 17 a - 68\) , \( -33 a^{2} + 24 a + 124\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(17a-68\right){x}-33a^{2}+24a+124$ |
| 35.1-a2 |
35.1-a |
$4$ |
$6$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5 \cdot 7^{4} \) |
$6.90422$ |
$(a-2), (-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1.565935262$ |
$73.27919487$ |
4.029158180 |
\( \frac{759176618264}{12005} a^{2} - \frac{2854803868001}{12005} a + \frac{1897150792291}{12005} \) |
\( \bigl[a\) , \( a + 1\) , \( a^{2} - 6\) , \( -5 a^{2} + 17 a - 8\) , \( -17 a^{2} + 67 a - 52\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-5a^{2}+17a-8\right){x}-17a^{2}+67a-52$ |
| 35.1-a3 |
35.1-a |
$4$ |
$6$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5^{2} \cdot 7^{2} \) |
$6.90422$ |
$(a-2), (-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.782967631$ |
$73.27919487$ |
4.029158180 |
\( -\frac{74247}{49} a^{2} + \frac{1682594}{245} a - \frac{1130363}{245} \) |
\( \bigl[a\) , \( a + 1\) , \( a^{2} - 6\) , \( 2 a + 2\) , \( a^{2} + 2 a - 9\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+2\right){x}+a^{2}+2a-9$ |
| 35.1-a4 |
35.1-a |
$4$ |
$6$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5^{6} \cdot 7^{6} \) |
$6.90422$ |
$(a-2), (-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$2.348902893$ |
$24.42639829$ |
4.029158180 |
\( \frac{2499774334544}{2941225} a^{2} + \frac{4172403380589}{2941225} a - \frac{1545634061053}{588245} \) |
\( \bigl[a\) , \( a + 1\) , \( a^{2} - 6\) , \( -8 a + 7\) , \( -8 a^{2} - 11 a + 9\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-8a+7\right){x}-8a^{2}-11a+9$ |
| 35.1-b1 |
35.1-b |
$4$ |
$6$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5^{3} \cdot 7^{12} \) |
$6.90422$ |
$(a-2), (-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$6.303107341$ |
0.442633748 |
\( -\frac{5523209449580259866763}{69206436005} a^{2} + \frac{761127012824843830457}{69206436005} a + \frac{44841915529379799234402}{69206436005} \) |
\( \bigl[a^{2} - 6\) , \( 0\) , \( a^{2} - 6\) , \( 399 a^{2} - 55 a - 3249\) , \( 9368 a^{2} - 1293 a - 76062\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(399a^{2}-55a-3249\right){x}+9368a^{2}-1293a-76062$ |
| 35.1-b2 |
35.1-b |
$4$ |
$6$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5^{6} \cdot 7^{6} \) |
$6.90422$ |
$(a-2), (-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$6.303107341$ |
0.442633748 |
\( \frac{2499774334544}{2941225} a^{2} + \frac{4172403380589}{2941225} a - \frac{1545634061053}{588245} \) |
\( \bigl[a^{2} - 6\) , \( 0\) , \( a^{2} - 6\) , \( 24 a^{2} - 5 a - 199\) , \( 188 a^{2} - 28 a - 1532\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(24a^{2}-5a-199\right){x}+188a^{2}-28a-1532$ |
| 35.1-b3 |
35.1-b |
$4$ |
$6$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5 \cdot 7^{4} \) |
$6.90422$ |
$(a-2), (-a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$170.1838982$ |
0.442633748 |
\( \frac{759176618264}{12005} a^{2} - \frac{2854803868001}{12005} a + \frac{1897150792291}{12005} \) |
\( \bigl[a^{2} - 6\) , \( 0\) , \( a^{2} - 6\) , \( 4 a^{2} - 39\) , \( 22 a^{2} - 4 a - 177\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(4a^{2}-39\right){x}+22a^{2}-4a-177$ |
| 35.1-b4 |
35.1-b |
$4$ |
$6$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5^{2} \cdot 7^{2} \) |
$6.90422$ |
$(a-2), (-a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$170.1838982$ |
0.442633748 |
\( -\frac{74247}{49} a^{2} + \frac{1682594}{245} a - \frac{1130363}{245} \) |
\( \bigl[a^{2} - 6\) , \( 0\) , \( a^{2} - 6\) , \( -a^{2} + 6\) , \( -a^{2} + 7\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(-a^{2}+6\right){x}-a^{2}+7$ |
| 41.2-a1 |
41.2-a |
$2$ |
$2$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
41.2 |
\( 41 \) |
\( 41^{2} \) |
$7.08871$ |
$(a^2-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.253478058$ |
$131.5925355$ |
5.791723440 |
\( \frac{3313179204}{1681} a^{2} - \frac{8551794321}{1681} a + \frac{4930460239}{1681} \) |
\( \bigl[a + 1\) , \( -a^{2} + 6\) , \( a^{2} - 5\) , \( -24 a^{2} + 79 a - 34\) , \( 178 a^{2} - 677 a + 455\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(-24a^{2}+79a-34\right){x}+178a^{2}-677a+455$ |
| 41.2-a2 |
41.2-a |
$2$ |
$2$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
41.2 |
\( 41 \) |
\( 41 \) |
$7.08871$ |
$(a^2-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$2.506956116$ |
$131.5925355$ |
5.791723440 |
\( \frac{6761}{41} a^{2} - \frac{58574}{41} a + \frac{49857}{41} \) |
\( \bigl[a + 1\) , \( -a^{2} + 6\) , \( a^{2} - 5\) , \( -4 a^{2} + 4 a + 16\) , \( 2 a^{2} - 11 a + 12\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(-4a^{2}+4a+16\right){x}+2a^{2}-11a+12$ |
| 41.2-b1 |
41.2-b |
$2$ |
$5$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
41.2 |
\( 41 \) |
\( - 41^{2} \) |
$7.08871$ |
$(a^2-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$0.839035517$ |
$46.00872539$ |
5.421760929 |
\( \frac{43107995}{1681} a^{2} - \frac{7041265}{1681} a - \frac{352452641}{1681} \) |
\( \bigl[a^{2} - 6\) , \( a^{2} - 5\) , \( a^{2} + a - 6\) , \( 2 a^{2} - a - 13\) , \( a^{2} - a - 9\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(2a^{2}-a-13\right){x}+a^{2}-a-9$ |
| 41.2-b2 |
41.2-b |
$2$ |
$5$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
41.2 |
\( 41 \) |
\( - 41^{10} \) |
$7.08871$ |
$(a^2-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 2 \) |
$4.195177589$ |
$9.201745078$ |
5.421760929 |
\( -\frac{63111328151676894474}{13422659310152401} a^{2} + \frac{234345761744066303849}{13422659310152401} a - \frac{146563149434045942468}{13422659310152401} \) |
\( \bigl[a^{2} - 6\) , \( a^{2} - 5\) , \( a^{2} + a - 6\) , \( -3 a^{2} + 4 a + 12\) , \( -11 a^{2} - 9 a + 85\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(-3a^{2}+4a+12\right){x}-11a^{2}-9a+85$ |
| 41.2-c1 |
41.2-c |
$2$ |
$2$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
41.2 |
\( 41 \) |
\( 41^{2} \) |
$7.08871$ |
$(a^2-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$9$ |
\( 2 \) |
$1$ |
$32.22522441$ |
3.394509510 |
\( \frac{3313179204}{1681} a^{2} - \frac{8551794321}{1681} a + \frac{4930460239}{1681} \) |
\( \bigl[a^{2} + a - 6\) , \( a - 1\) , \( 1\) , \( a^{2} + 9 a - 9\) , \( 4 a^{2} + 10 a - 35\bigr] \) |
${y}^2+\left(a^{2}+a-6\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(a^{2}+9a-9\right){x}+4a^{2}+10a-35$ |
| 41.2-c2 |
41.2-c |
$2$ |
$2$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
41.2 |
\( 41 \) |
\( 41 \) |
$7.08871$ |
$(a^2-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$9$ |
\( 1 \) |
$1$ |
$64.45044882$ |
3.394509510 |
\( \frac{6761}{41} a^{2} - \frac{58574}{41} a + \frac{49857}{41} \) |
\( \bigl[a^{2} + a - 6\) , \( a - 1\) , \( 1\) , \( a^{2} + 4 a + 6\) , \( 2 a^{2} + 5 a - 2\bigr] \) |
${y}^2+\left(a^{2}+a-6\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(a^{2}+4a+6\right){x}+2a^{2}+5a-2$ |
| 41.2-d1 |
41.2-d |
$2$ |
$5$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
41.2 |
\( 41 \) |
\( - 41^{10} \) |
$7.08871$ |
$(a^2-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$1.952952865$ |
0.457151687 |
\( -\frac{63111328151676894474}{13422659310152401} a^{2} + \frac{234345761744066303849}{13422659310152401} a - \frac{146563149434045942468}{13422659310152401} \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( -20 a^{2} + 69 a - 45\) , \( -150 a^{2} + 468 a - 293\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-20a^{2}+69a-45\right){x}-150a^{2}+468a-293$ |
| 41.2-d2 |
41.2-d |
$2$ |
$5$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
41.2 |
\( 41 \) |
\( - 41^{2} \) |
$7.08871$ |
$(a^2-5)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$244.1191082$ |
0.457151687 |
\( \frac{43107995}{1681} a^{2} - \frac{7041265}{1681} a - \frac{352452641}{1681} \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( -a\) , \( -a\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}-a{x}-a$ |
| 41.2-e1 |
41.2-e |
$1$ |
$1$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
41.2 |
\( 41 \) |
\( -41 \) |
$7.08871$ |
$(a^2-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.188790066$ |
$323.4495401$ |
4.288204583 |
\( \frac{12575}{41} a^{2} - \frac{3030}{41} a - \frac{26442}{41} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - 6\) , \( a^{2} + a - 5\) , \( a^{2} - a - 7\) , \( -a - 2\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(a^{2}-a-7\right){x}-a-2$ |
| 41.2-f1 |
41.2-f |
$1$ |
$1$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
41.2 |
\( 41 \) |
\( -41 \) |
$7.08871$ |
$(a^2-5)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.204306114$ |
$133.5347349$ |
5.747602021 |
\( \frac{12575}{41} a^{2} - \frac{3030}{41} a - \frac{26442}{41} \) |
\( \bigl[a^{2} + a - 5\) , \( -a^{2} - a + 7\) , \( a^{2} + a - 6\) , \( -2 a^{2} - a + 14\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+\left(-a^{2}-a+7\right){x}^{2}+\left(-2a^{2}-a+14\right){x}$ |
| 49.2-a1 |
49.2-a |
$1$ |
$1$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
49.2 |
\( 7^{2} \) |
\( - 7^{2} \) |
$7.30246$ |
$(-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$152.8342774$ |
3.577579832 |
\( 556 a^{2} - 49 a - 4438 \) |
\( \bigl[a^{2} + a - 6\) , \( a^{2} - a - 5\) , \( 1\) , \( 2 a^{2} + a - 1\) , \( 2 a^{2} + 2 a - 3\bigr] \) |
${y}^2+\left(a^{2}+a-6\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(2a^{2}+a-1\right){x}+2a^{2}+2a-3$ |
| 49.2-b1 |
49.2-b |
$2$ |
$2$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{6} \) |
$7.30246$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$63.01388175$ |
0.737521701 |
\( 4071 a^{2} + 4201 a - 19798 \) |
\( \bigl[1\) , \( a^{2} - 7\) , \( a^{2} + a - 6\) , \( -5 a^{2} - 6 a + 23\) , \( 6 a^{2} + 8 a - 24\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+\left(a^{2}-7\right){x}^{2}+\left(-5a^{2}-6a+23\right){x}+6a^{2}+8a-24$ |
| 49.2-b2 |
49.2-b |
$2$ |
$2$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{6} \) |
$7.30246$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$63.01388175$ |
0.737521701 |
\( 33751039 a^{2} + 117637124 a + 66126589 \) |
\( \bigl[1\) , \( a^{2} - 7\) , \( a^{2} + a - 6\) , \( -50 a^{2} - 91 a + 128\) , \( 410 a^{2} + 783 a - 990\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+\left(a^{2}-7\right){x}^{2}+\left(-50a^{2}-91a+128\right){x}+410a^{2}+783a-990$ |
| 49.2-c1 |
49.2-c |
$1$ |
$1$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
49.2 |
\( 7^{2} \) |
\( - 7^{2} \) |
$7.30246$ |
$(-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$101.1151661$ |
2.366927009 |
\( 556 a^{2} - 49 a - 4438 \) |
\( \bigl[a + 1\) , \( 0\) , \( a^{2} + a - 5\) , \( -a^{2} - a + 5\) , \( -a - 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(-a^{2}-a+5\right){x}-a-2$ |
| 49.2-d1 |
49.2-d |
$2$ |
$2$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{6} \) |
$7.30246$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$118.1981960$ |
1.383405246 |
\( 33751039 a^{2} + 117637124 a + 66126589 \) |
\( \bigl[a\) , \( a - 1\) , \( a^{2} - 6\) , \( -27 a - 72\) , \( -4 a^{2} + 92 a + 286\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-27a-72\right){x}-4a^{2}+92a+286$ |
| 49.2-d2 |
49.2-d |
$2$ |
$2$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{6} \) |
$7.30246$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$118.1981960$ |
1.383405246 |
\( 4071 a^{2} + 4201 a - 19798 \) |
\( \bigl[a\) , \( a - 1\) , \( a^{2} - 6\) , \( -2 a - 2\) , \( -1\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a-2\right){x}-1$ |
| 55.1-a1 |
55.1-a |
$4$ |
$4$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( - 5^{3} \cdot 11^{3} \) |
$7.44441$ |
$(a-2), (a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 3 \) |
$1$ |
$183.6867657$ |
3.224836468 |
\( -\frac{155241403769}{6655} a^{2} + \frac{4279876738}{1331} a + \frac{252074062995}{1331} \) |
\( \bigl[a^{2} - 6\) , \( -a - 1\) , \( a + 1\) , \( -109 a^{2} - 206 a + 272\) , \( 497 a^{2} + 955 a - 1189\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-109a^{2}-206a+272\right){x}+497a^{2}+955a-1189$ |
| 55.1-a2 |
55.1-a |
$4$ |
$4$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{12} \cdot 11^{3} \) |
$7.44441$ |
$(a-2), (a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$4$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$11.48042286$ |
3.224836468 |
\( \frac{12753842239372040877}{831875} a^{2} - \frac{48225896996235685519}{831875} a + \frac{32099167947172480586}{831875} \) |
\( \bigl[a^{2} - 6\) , \( -a - 1\) , \( a + 1\) , \( -329 a^{2} - 486 a + 677\) , \( -95993 a^{2} - 185350 a + 231171\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-329a^{2}-486a+677\right){x}-95993a^{2}-185350a+231171$ |
| 55.1-a3 |
55.1-a |
$4$ |
$4$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{6} \cdot 11^{6} \) |
$7.44441$ |
$(a-2), (a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3Ns |
$4$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$45.92169144$ |
3.224836468 |
\( \frac{38401441560864}{44289025} a^{2} - \frac{143054085407499}{44289025} a + \frac{95412829327063}{44289025} \) |
\( \bigl[a^{2} - 6\) , \( -a - 1\) , \( a + 1\) , \( -994 a^{2} - 1896 a + 2387\) , \( -40006 a^{2} - 76786 a + 95948\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-994a^{2}-1896a+2387\right){x}-40006a^{2}-76786a+95948$ |
| 55.1-a4 |
55.1-a |
$4$ |
$4$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{3} \cdot 11^{12} \) |
$7.44441$ |
$(a-2), (a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$16$ |
\( 2 \cdot 3 \) |
$1$ |
$5.740211430$ |
3.224836468 |
\( \frac{17152936432430680778629}{15692141883605} a^{2} + \frac{6583602216565772008917}{3138428376721} a - \frac{8226561740559112701822}{3138428376721} \) |
\( \bigl[a^{2} - 6\) , \( -a - 1\) , \( a + 1\) , \( -15819 a^{2} - 30346 a + 37937\) , \( -2609091 a^{2} - 5007086 a + 6256633\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-15819a^{2}-30346a+37937\right){x}-2609091a^{2}-5007086a+6256633$ |
| 55.1-b1 |
55.1-b |
$2$ |
$2$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( - 5 \cdot 11^{3} \) |
$7.44441$ |
$(a-2), (a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$146.3705383$ |
3.426275145 |
\( -\frac{86056}{6655} a^{2} + \frac{1570644}{6655} a + \frac{10210811}{6655} \) |
\( \bigl[a^{2} + a - 5\) , \( -a^{2} + 5\) , \( a + 1\) , \( -3 a^{2} - a + 23\) , \( -3 a^{2} - 2 a + 16\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-3a^{2}-a+23\right){x}-3a^{2}-2a+16$ |
| 55.1-b2 |
55.1-b |
$2$ |
$2$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{2} \cdot 11^{6} \) |
$7.44441$ |
$(a-2), (a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$146.3705383$ |
3.426275145 |
\( -\frac{296729465242}{8857805} a^{2} + \frac{144963398044}{8857805} a + \frac{545956197079}{1771561} \) |
\( \bigl[a^{2} + a - 5\) , \( -a^{2} + 5\) , \( a + 1\) , \( -8 a^{2} - 11 a + 33\) , \( 5 a^{2} + 12 a - 6\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-8a^{2}-11a+33\right){x}+5a^{2}+12a-6$ |
| 55.1-c1 |
55.1-c |
$2$ |
$2$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{2} \cdot 11^{6} \) |
$7.44441$ |
$(a-2), (a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.504313358$ |
$58.02562122$ |
6.164975369 |
\( -\frac{296729465242}{8857805} a^{2} + \frac{144963398044}{8857805} a + \frac{545956197079}{1771561} \) |
\( \bigl[a + 1\) , \( a^{2} - a - 6\) , \( 1\) , \( 16 a^{2} - 7 a - 133\) , \( 51 a^{2} - 6 a - 406\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(16a^{2}-7a-133\right){x}+51a^{2}-6a-406$ |
| 55.1-c2 |
55.1-c |
$2$ |
$2$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( - 5 \cdot 11^{3} \) |
$7.44441$ |
$(a-2), (a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$1.008626716$ |
$116.0512424$ |
6.164975369 |
\( -\frac{86056}{6655} a^{2} + \frac{1570644}{6655} a + \frac{10210811}{6655} \) |
\( \bigl[a + 1\) , \( a^{2} - a - 6\) , \( 1\) , \( a^{2} - 2 a - 3\) , \( -2 a^{2} - a + 18\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(a^{2}-2a-3\right){x}-2a^{2}-a+18$ |
| 55.1-d1 |
55.1-d |
$4$ |
$4$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( - 5^{3} \cdot 11^{3} \) |
$7.44441$ |
$(a-2), (a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 3^{2} \) |
$1.482586566$ |
$22.88309867$ |
5.360523849 |
\( -\frac{155241403769}{6655} a^{2} + \frac{4279876738}{1331} a + \frac{252074062995}{1331} \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} - a + 7\) , \( a^{2} + a - 5\) , \( -33 a^{2} - 58 a + 99\) , \( 67 a^{2} + 136 a - 138\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(-a^{2}-a+7\right){x}^{2}+\left(-33a^{2}-58a+99\right){x}+67a^{2}+136a-138$ |
| 55.1-d2 |
55.1-d |
$4$ |
$4$ |
3.3.1825.1 |
$3$ |
$[3, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{12} \cdot 11^{3} \) |
$7.44441$ |
$(a-2), (a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$4$ |
\( 2^{2} \cdot 3^{2} \) |
$1.482586566$ |
$1.430193667$ |
5.360523849 |
\( \frac{12753842239372040877}{831875} a^{2} - \frac{48225896996235685519}{831875} a + \frac{32099167947172480586}{831875} \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} - a + 7\) , \( a^{2} + a - 5\) , \( -88 a^{2} - 153 a + 224\) , \( -13618 a^{2} - 26089 a + 32652\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(-a^{2}-a+7\right){x}^{2}+\left(-88a^{2}-153a+224\right){x}-13618a^{2}-26089a+32652$ |
*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.
