| 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 |
| 20412.2-a1 |
20412.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{4} \cdot 3^{10} \cdot 7^{2} \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2^{3} \cdot 3 \) |
$0.014011256$ |
$3.226174651$ |
3.280327288 |
\( -\frac{3}{28} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 0\) , \( 4\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+4$ |
| 20412.2-b1 |
20412.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{10} \cdot 3^{10} \cdot 7^{14} \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$0.319584965$ |
1.449501157 |
\( \frac{38983348653}{26353376} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 441\) , \( -1571\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+441{x}-1571$ |
| 20412.2-c1 |
20412.2-c |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{3} \cdot 3^{6} \cdot 7^{3} \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.622784284$ |
$3.834222525$ |
2.406770454 |
\( \frac{616869}{196} a + \frac{610767}{196} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -3 a\) , \( 3 a - 2\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-3a{x}+3a-2$ |
| 20412.2-c2 |
20412.2-c |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{9} \cdot 3^{18} \cdot 7 \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$0.207594761$ |
$1.278074175$ |
2.406770454 |
\( -\frac{491535}{448} a + \frac{2054781}{448} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 27 a - 15\) , \( 27 a + 35\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(27a-15\right){x}+27a+35$ |
| 20412.2-d1 |
20412.2-d |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{2} \cdot 3^{10} \cdot 7^{2} \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$3.818486457$ |
$0.678569946$ |
2.611593553 |
\( -\frac{545407363875}{14} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -1062\) , \( 13590\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-1062{x}+13590$ |
| 20412.2-d2 |
20412.2-d |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{6} \cdot 3^{6} \cdot 7^{6} \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1.272828819$ |
$2.035709838$ |
2.611593553 |
\( -\frac{7414875}{2744} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -12\) , \( 24\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-12{x}+24$ |
| 20412.2-d3 |
20412.2-d |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{18} \cdot 3^{18} \cdot 7^{2} \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$0.424276273$ |
$0.678569946$ |
2.611593553 |
\( \frac{4492125}{3584} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 93\) , \( -235\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+93{x}-235$ |
| 20412.2-e1 |
20412.2-e |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{9} \cdot 3^{18} \cdot 7 \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$0.207594761$ |
$1.278074175$ |
2.406770454 |
\( \frac{491535}{448} a + \frac{781623}{224} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -27 a + 12\) , \( -27 a + 62\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-27a+12\right){x}-27a+62$ |
| 20412.2-e2 |
20412.2-e |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{3} \cdot 3^{6} \cdot 7^{3} \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.622784284$ |
$3.834222525$ |
2.406770454 |
\( -\frac{616869}{196} a + \frac{306909}{49} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 3 a - 3\) , \( -3 a + 1\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(3a-3\right){x}-3a+1$ |
| 20412.2-f1 |
20412.2-f |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{4} \cdot 3^{6} \cdot 7^{2} \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{3} \) |
$1.302973442$ |
$1.513949445$ |
2.650973497 |
\( -\frac{11527859979}{28} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -141\) , \( 681\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-141{x}+681$ |
| 20412.2-f2 |
20412.2-f |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{12} \cdot 3^{18} \cdot 7^{6} \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$0.434324480$ |
$0.504649815$ |
2.650973497 |
\( -\frac{5000211}{21952} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -96\) , \( 1088\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-96{x}+1088$ |
| 20412.2-f3 |
20412.2-f |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{36} \cdot 3^{22} \cdot 7^{2} \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{3} \) |
$1.302973442$ |
$0.168216605$ |
2.650973497 |
\( \frac{381790581}{1835008} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 849\) , \( -25939\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+849{x}-25939$ |
| 20412.2-g1 |
20412.2-g |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{10} \cdot 3^{18} \cdot 7 \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$1.145886702$ |
2.598626782 |
\( \frac{17726013}{3584} a - \frac{32963247}{3584} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -14 a - 42\) , \( -61 a - 86\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-14a-42\right){x}-61a-86$ |
| 20412.2-g2 |
20412.2-g |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{6} \cdot 3^{6} \cdot 7^{3} \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$3.437660108$ |
2.598626782 |
\( -\frac{12825}{196} a + \frac{746901}{392} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( a + 3\) , \( -1\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(a+3\right){x}-1$ |
| 20412.2-g3 |
20412.2-g |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{10} \cdot 3^{10} \cdot 7 \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{3} \) |
$1$ |
$1.145886702$ |
2.598626782 |
\( \frac{35574823797}{3584} a + \frac{53088883473}{1792} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 76 a + 123\) , \( -528 a + 977\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(76a+123\right){x}-528a+977$ |
| 20412.2-h1 |
20412.2-h |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{15} \cdot 3^{6} \cdot 7^{3} \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{3} \) |
$0.256876819$ |
$1.993481702$ |
4.645146237 |
\( \frac{40060305}{25088} a - \frac{16131447}{12544} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -8 a - 3\) , \( 16 a - 9\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-8a-3\right){x}+16a-9$ |
| 20412.2-h2 |
20412.2-h |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{21} \cdot 3^{18} \cdot 7 \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$0.770630458$ |
$0.664493900$ |
4.645146237 |
\( -\frac{1331618265}{1835008} a + \frac{2726373411}{1835008} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 67 a + 12\) , \( -169 a + 346\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(67a+12\right){x}-169a+346$ |
| 20412.2-h3 |
20412.2-h |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{29} \cdot 3^{10} \cdot 7 \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{3} \) |
$0.770630458$ |
$0.664493900$ |
4.645146237 |
\( \frac{3839232553671}{939524096} a + \frac{58385000676603}{469762048} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -23 a + 267\) , \( 1180 a - 381\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-23a+267\right){x}+1180a-381$ |
| 20412.2-i1 |
20412.2-i |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{10} \cdot 3^{6} \cdot 7 \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$3.437660108$ |
2.598626782 |
\( -\frac{17726013}{3584} a - \frac{7618617}{1792} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( a - 6\) , \( -3 a + 8\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(a-6\right){x}-3a+8$ |
| 20412.2-i2 |
20412.2-i |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{6} \cdot 3^{18} \cdot 7^{3} \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3^{3} \) |
$1$ |
$1.145886702$ |
2.598626782 |
\( \frac{12825}{196} a + \frac{721251}{392} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -14 a + 39\) , \( 20 a - 5\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-14a+39\right){x}+20a-5$ |
| 20412.2-i3 |
20412.2-i |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{10} \cdot 3^{22} \cdot 7 \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$0.381962234$ |
2.598626782 |
\( -\frac{35574823797}{3584} a + \frac{141752590743}{3584} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -689 a + 1794\) , \( -13561 a - 13910\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-689a+1794\right){x}-13561a-13910$ |
| 20412.2-j1 |
20412.2-j |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{23} \cdot 3^{18} \cdot 7^{3} \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3 \cdot 5 \) |
$0.615621778$ |
$0.182954823$ |
5.108460803 |
\( \frac{300962315713599}{12845056} a - \frac{610227325676133}{12845056} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -3983 a + 7572\) , \( 83585 a + 191398\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-3983a+7572\right){x}+83585a+191398$ |
| 20412.2-j2 |
20412.2-j |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{47} \cdot 3^{10} \cdot 7^{3} \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{3} \cdot 5 \) |
$0.615621778$ |
$0.182954823$ |
5.108460803 |
\( -\frac{35698603099504922097}{1724034232352768} a - \frac{24925846281312461661}{862017116176384} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 1687 a - 2613\) , \( 43482 a - 33673\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(1687a-2613\right){x}+43482a-33673$ |
| 20412.2-j3 |
20412.2-j |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{21} \cdot 3^{6} \cdot 7^{9} \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{3} \cdot 5 \) |
$0.205207259$ |
$0.548864471$ |
5.108460803 |
\( -\frac{128180412495}{550731776} a + \frac{402765966621}{275365888} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -98 a + 117\) , \( 306 a - 325\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-98a+117\right){x}+306a-325$ |
| 20412.2-k1 |
20412.2-k |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{23} \cdot 3^{6} \cdot 7^{3} \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{3} \) |
$1$ |
$0.548864471$ |
2.489415246 |
\( -\frac{300962315713599}{12845056} a - \frac{154632504981267}{6422528} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 442 a + 399\) , \( 2948 a - 10317\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(442a+399\right){x}+2948a-10317$ |
| 20412.2-k2 |
20412.2-k |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{47} \cdot 3^{22} \cdot 7^{3} \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$9$ |
\( 2 \cdot 3 \) |
$1$ |
$0.060984941$ |
2.489415246 |
\( \frac{35698603099504922097}{1724034232352768} a - \frac{85550295662129845419}{1724034232352768} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -15188 a - 8331\) , \( 1189208 a - 256505\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-15188a-8331\right){x}+1189208a-256505$ |
| 20412.2-k3 |
20412.2-k |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{21} \cdot 3^{18} \cdot 7^{9} \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{4} \) |
$1$ |
$0.182954823$ |
2.489415246 |
\( \frac{128180412495}{550731776} a + \frac{677351520747}{550731776} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 877 a + 174\) , \( 7391 a + 346\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(877a+174\right){x}+7391a+346$ |
| 20412.2-l1 |
20412.2-l |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{15} \cdot 3^{18} \cdot 7^{3} \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{3} \) |
$1$ |
$0.664493900$ |
3.013861045 |
\( -\frac{40060305}{25088} a + \frac{7797411}{25088} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 67 a - 96\) , \( 371 a - 86\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(67a-96\right){x}+371a-86$ |
| 20412.2-l2 |
20412.2-l |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{21} \cdot 3^{6} \cdot 7 \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$1.993481702$ |
3.013861045 |
\( \frac{1331618265}{1835008} a + \frac{697377573}{917504} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -8 a + 9\) , \( -4 a - 9\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-8a+9\right){x}-4a-9$ |
| 20412.2-l3 |
20412.2-l |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{29} \cdot 3^{22} \cdot 7 \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$0.221497966$ |
3.013861045 |
\( -\frac{3839232553671}{939524096} a + \frac{120609233906877}{939524096} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 202 a + 2199\) , \( 31664 a - 23765\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(202a+2199\right){x}+31664a-23765$ |
| 20412.2-m1 |
20412.2-m |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{15} \cdot 3^{6} \cdot 7^{3} \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{3} \) |
$0.256876819$ |
$1.993481702$ |
4.645146237 |
\( -\frac{40060305}{25088} a + \frac{7797411}{25088} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 7 a - 11\) , \( -17 a + 7\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(7a-11\right){x}-17a+7$ |
| 20412.2-m2 |
20412.2-m |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{21} \cdot 3^{18} \cdot 7 \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$0.770630458$ |
$0.664493900$ |
4.645146237 |
\( \frac{1331618265}{1835008} a + \frac{697377573}{917504} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -68 a + 79\) , \( 168 a + 177\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-68a+79\right){x}+168a+177$ |
| 20412.2-m3 |
20412.2-m |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{29} \cdot 3^{10} \cdot 7 \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{3} \) |
$0.770630458$ |
$0.664493900$ |
4.645146237 |
\( -\frac{3839232553671}{939524096} a + \frac{120609233906877}{939524096} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 22 a + 244\) , \( -1181 a + 799\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(22a+244\right){x}-1181a+799$ |
| 20412.2-n1 |
20412.2-n |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{23} \cdot 3^{18} \cdot 7^{3} \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3 \cdot 5 \) |
$0.615621778$ |
$0.182954823$ |
5.108460803 |
\( -\frac{300962315713599}{12845056} a - \frac{154632504981267}{6422528} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 3982 a + 3589\) , \( -83586 a + 274983\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(3982a+3589\right){x}-83586a+274983$ |
| 20412.2-n2 |
20412.2-n |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{47} \cdot 3^{10} \cdot 7^{3} \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{3} \cdot 5 \) |
$0.615621778$ |
$0.182954823$ |
5.108460803 |
\( \frac{35698603099504922097}{1724034232352768} a - \frac{85550295662129845419}{1724034232352768} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -1688 a - 926\) , \( -43483 a + 9809\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-1688a-926\right){x}-43483a+9809$ |
| 20412.2-n3 |
20412.2-n |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{21} \cdot 3^{6} \cdot 7^{9} \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{3} \cdot 5 \) |
$0.205207259$ |
$0.548864471$ |
5.108460803 |
\( \frac{128180412495}{550731776} a + \frac{677351520747}{550731776} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 97 a + 19\) , \( -307 a - 19\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(97a+19\right){x}-307a-19$ |
| 20412.2-o1 |
20412.2-o |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{23} \cdot 3^{6} \cdot 7^{3} \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{3} \) |
$1$ |
$0.548864471$ |
2.489415246 |
\( \frac{300962315713599}{12845056} a - \frac{610227325676133}{12845056} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -443 a + 841\) , \( -2949 a - 7369\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-443a+841\right){x}-2949a-7369$ |
| 20412.2-o2 |
20412.2-o |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{47} \cdot 3^{22} \cdot 7^{3} \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$9$ |
\( 2 \cdot 3 \) |
$1$ |
$0.060984941$ |
2.489415246 |
\( -\frac{35698603099504922097}{1724034232352768} a - \frac{24925846281312461661}{862017116176384} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 15187 a - 23519\) , \( -1189209 a + 932703\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(15187a-23519\right){x}-1189209a+932703$ |
| 20412.2-o3 |
20412.2-o |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{21} \cdot 3^{18} \cdot 7^{9} \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{4} \) |
$1$ |
$0.182954823$ |
2.489415246 |
\( -\frac{128180412495}{550731776} a + \frac{402765966621}{275365888} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -878 a + 1051\) , \( -7392 a + 7737\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-878a+1051\right){x}-7392a+7737$ |
| 20412.2-p1 |
20412.2-p |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{10} \cdot 3^{18} \cdot 7 \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$1.145886702$ |
2.598626782 |
\( -\frac{17726013}{3584} a - \frac{7618617}{1792} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 13 a - 56\) , \( 60 a - 147\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(13a-56\right){x}+60a-147$ |
| 20412.2-p2 |
20412.2-p |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{6} \cdot 3^{6} \cdot 7^{3} \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$3.437660108$ |
2.598626782 |
\( \frac{12825}{196} a + \frac{721251}{392} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -2 a + 4\) , \( -a - 1\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-2a+4\right){x}-a-1$ |
| 20412.2-p3 |
20412.2-p |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{10} \cdot 3^{10} \cdot 7 \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{3} \) |
$1$ |
$1.145886702$ |
2.598626782 |
\( -\frac{35574823797}{3584} a + \frac{141752590743}{3584} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -77 a + 199\) , \( 527 a + 449\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-77a+199\right){x}+527a+449$ |
| 20412.2-q1 |
20412.2-q |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{15} \cdot 3^{18} \cdot 7^{3} \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{3} \) |
$1$ |
$0.664493900$ |
3.013861045 |
\( \frac{40060305}{25088} a - \frac{16131447}{12544} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -68 a - 29\) , \( -372 a + 285\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-68a-29\right){x}-372a+285$ |
| 20412.2-q2 |
20412.2-q |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{21} \cdot 3^{6} \cdot 7 \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$1.993481702$ |
3.013861045 |
\( -\frac{1331618265}{1835008} a + \frac{2726373411}{1835008} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 7 a + 1\) , \( 3 a - 13\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(7a+1\right){x}+3a-13$ |
| 20412.2-q3 |
20412.2-q |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{29} \cdot 3^{22} \cdot 7 \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$0.221497966$ |
3.013861045 |
\( \frac{3839232553671}{939524096} a + \frac{58385000676603}{469762048} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -203 a + 2401\) , \( -31665 a + 7899\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-203a+2401\right){x}-31665a+7899$ |
| 20412.2-r1 |
20412.2-r |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{10} \cdot 3^{6} \cdot 7 \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$3.437660108$ |
2.598626782 |
\( \frac{17726013}{3584} a - \frac{32963247}{3584} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -2 a - 5\) , \( 2 a + 5\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-2a-5\right){x}+2a+5$ |
| 20412.2-r2 |
20412.2-r |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{6} \cdot 3^{18} \cdot 7^{3} \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3^{3} \) |
$1$ |
$1.145886702$ |
2.598626782 |
\( -\frac{12825}{196} a + \frac{746901}{392} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 13 a + 25\) , \( -21 a + 15\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(13a+25\right){x}-21a+15$ |
| 20412.2-r3 |
20412.2-r |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{10} \cdot 3^{22} \cdot 7 \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$0.381962234$ |
2.598626782 |
\( \frac{35574823797}{3584} a + \frac{53088883473}{1792} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 688 a + 1105\) , \( 13560 a - 27471\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(688a+1105\right){x}+13560a-27471$ |
| 20412.2-s1 |
20412.2-s |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{10} \cdot 3^{22} \cdot 7^{14} \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2 \cdot 5^{2} \) |
$1$ |
$0.106528321$ |
4.026392104 |
\( \frac{38983348653}{26353376} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 3967\) , \( 38449\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+3967{x}+38449$ |
| 20412.2-t1 |
20412.2-t |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20412.2 |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
\( 2^{4} \cdot 3^{22} \cdot 7^{2} \) |
$2.82591$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$1.075391550$ |
6.503356810 |
\( -\frac{3}{28} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -2\) , \( -107\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-2{x}-107$ |
*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.
