| 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 |
| 14.1-a1 |
14.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{18} \cdot 7^{3} \) |
$2.24040$ |
$(2,a), (a+7)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$24.21346718$ |
3.736219100 |
\( \frac{9930171131}{392} a - \frac{9193553137}{56} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 48 a - 204\) , \( -272 a + 1976\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(48a-204\right){x}-272a+1976$ |
| 14.1-a2 |
14.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{14} \cdot 7 \) |
$2.24040$ |
$(2,a), (a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$24.21346718$ |
3.736219100 |
\( \frac{225}{14} a - \frac{169}{2} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 8 a + 56\) , \( 16 a + 112\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(8a+56\right){x}+16a+112$ |
| 14.1-b1 |
14.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{48} \cdot 7^{2} \) |
$2.24040$ |
$(2,a), (a+7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$7.027708105$ |
1.084398903 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -35476 a - 229804\) , \( 9223680 a + 59776488\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-35476a-229804\right){x}+9223680a+59776488$ |
| 14.1-b2 |
14.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{16} \cdot 7^{2} \) |
$2.24040$ |
$(2,a), (a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$7.027708105$ |
1.084398903 |
\( -\frac{15625}{28} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -116 a - 644\) , \( -3360 a - 21560\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-116a-644\right){x}-3360a-21560$ |
| 14.1-b3 |
14.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{24} \cdot 7^{6} \) |
$2.24040$ |
$(2,a), (a+7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$7.027708105$ |
1.084398903 |
\( \frac{9938375}{21952} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 924 a + 6096\) , \( 67680 a + 438832\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(924a+6096\right){x}+67680a+438832$ |
| 14.1-b4 |
14.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{18} \cdot 7^{12} \) |
$2.24040$ |
$(2,a), (a+7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$7.027708105$ |
1.084398903 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -7396 a - 47824\) , \( 708960 a + 4594800\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-7396a-47824\right){x}+708960a+4594800$ |
| 14.1-b5 |
14.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{14} \cdot 7^{4} \) |
$2.24040$ |
$(2,a), (a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$7.027708105$ |
1.084398903 |
\( \frac{128787625}{98} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -2196 a - 14124\) , \( -145440 a - 942344\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2196a-14124\right){x}-145440a-942344$ |
| 14.1-b6 |
14.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{30} \cdot 7^{4} \) |
$2.24040$ |
$(2,a), (a+7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$7.027708105$ |
1.084398903 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -567956 a - 3680684\) , \( 592166400 a + 3837677032\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-567956a-3680684\right){x}+592166400a+3837677032$ |
| 14.1-c1 |
14.1-c |
$6$ |
$18$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{36} \cdot 7^{2} \) |
$2.24040$ |
$(2,a), (a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$3.484059793$ |
$7.027708105$ |
3.778110619 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -8871 a - 57416\) , \( 1135220 a + 7357190\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-8871a-57416\right){x}+1135220a+7357190$ |
| 14.1-c2 |
14.1-c |
$6$ |
$18$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{4} \cdot 7^{2} \) |
$2.24040$ |
$(2,a), (a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$3.484059793$ |
$7.027708105$ |
3.778110619 |
\( -\frac{15625}{28} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -31 a - 126\) , \( -480 a - 2986\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-31a-126\right){x}-480a-2986$ |
| 14.1-c3 |
14.1-c |
$6$ |
$18$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{12} \cdot 7^{6} \) |
$2.24040$ |
$(2,a), (a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$1.161353264$ |
$7.027708105$ |
3.778110619 |
\( \frac{9938375}{21952} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 229 a + 1559\) , \( 8920 a + 57933\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(229a+1559\right){x}+8920a+57933$ |
| 14.1-c4 |
14.1-c |
$6$ |
$18$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{6} \cdot 7^{12} \) |
$2.24040$ |
$(2,a), (a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.580676632$ |
$7.027708105$ |
3.778110619 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -1851 a - 11921\) , \( 84920 a + 550469\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1851a-11921\right){x}+84920a+550469$ |
| 14.1-c5 |
14.1-c |
$6$ |
$18$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{2} \cdot 7^{4} \) |
$2.24040$ |
$(2,a), (a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1.742029896$ |
$7.027708105$ |
3.778110619 |
\( \frac{128787625}{98} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -551 a - 3496\) , \( -19280 a - 124824\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-551a-3496\right){x}-19280a-124824$ |
| 14.1-c6 |
14.1-c |
$6$ |
$18$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{18} \cdot 7^{4} \) |
$2.24040$ |
$(2,a), (a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1.742029896$ |
$7.027708105$ |
3.778110619 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -141991 a - 920136\) , \( 73736820 a + 477869318\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-141991a-920136\right){x}+73736820a+477869318$ |
| 14.1-d1 |
14.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{6} \cdot 7^{3} \) |
$2.24040$ |
$(2,a), (a+7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$0.089361065$ |
$24.21346718$ |
2.003235112 |
\( \frac{9930171131}{392} a - \frac{9193553137}{56} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 14 a - 16\) , \( -8 a + 176\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(14a-16\right){x}-8a+176$ |
| 14.1-d2 |
14.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{2} \cdot 7 \) |
$2.24040$ |
$(2,a), (a+7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.268083195$ |
$24.21346718$ |
2.003235112 |
\( \frac{225}{14} a - \frac{169}{2} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 4 a + 49\) , \( 8 a + 73\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(4a+49\right){x}+8a+73$ |
| 14.1-e1 |
14.1-e |
$2$ |
$3$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{6} \cdot 7^{3} \) |
$2.24040$ |
$(2,a), (a+7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$0.089361065$ |
$24.21346718$ |
2.003235112 |
\( -\frac{9930171131}{392} a - \frac{9193553137}{56} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -14 a - 16\) , \( 8 a + 176\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-14a-16\right){x}+8a+176$ |
| 14.1-e2 |
14.1-e |
$2$ |
$3$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{2} \cdot 7 \) |
$2.24040$ |
$(2,a), (a+7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.268083195$ |
$24.21346718$ |
2.003235112 |
\( -\frac{225}{14} a - \frac{169}{2} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -4 a + 49\) , \( -8 a + 73\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a+49\right){x}-8a+73$ |
| 14.1-f1 |
14.1-f |
$2$ |
$3$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{6} \cdot 7^{3} \) |
$2.24040$ |
$(2,a), (a+7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$1.618106300$ |
$2.052397443$ |
3.074645990 |
\( -\frac{9930171131}{392} a - \frac{9193553137}{56} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 9 a - 59\) , \( 353 a - 2288\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(9a-59\right){x}+353a-2288$ |
| 14.1-f2 |
14.1-f |
$2$ |
$3$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{2} \cdot 7 \) |
$2.24040$ |
$(2,a), (a+7)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$4.854318900$ |
$18.47157698$ |
3.074645990 |
\( -\frac{225}{14} a - \frac{169}{2} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -a + 6\) , \( -13 a + 84\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+6\right){x}-13a+84$ |
| 14.1-g1 |
14.1-g |
$2$ |
$3$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{18} \cdot 7^{3} \) |
$2.24040$ |
$(2,a), (a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$2.052397443$ |
2.850226208 |
\( -\frac{9930171131}{392} a - \frac{9193553137}{56} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 36 a - 225\) , \( 2932 a - 18983\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(36a-225\right){x}+2932a-18983$ |
| 14.1-g2 |
14.1-g |
$2$ |
$3$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{14} \cdot 7 \) |
$2.24040$ |
$(2,a), (a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$18.47157698$ |
2.850226208 |
\( -\frac{225}{14} a - \frac{169}{2} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -4 a + 35\) , \( -116 a + 773\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-4a+35\right){x}-116a+773$ |
| 14.1-h1 |
14.1-h |
$2$ |
$3$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{18} \cdot 7^{3} \) |
$2.24040$ |
$(2,a), (a+7)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$24.21346718$ |
3.736219100 |
\( -\frac{9930171131}{392} a - \frac{9193553137}{56} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -48 a - 204\) , \( 272 a + 1976\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-48a-204\right){x}+272a+1976$ |
| 14.1-h2 |
14.1-h |
$2$ |
$3$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{14} \cdot 7 \) |
$2.24040$ |
$(2,a), (a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$24.21346718$ |
3.736219100 |
\( -\frac{225}{14} a - \frac{169}{2} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -8 a + 56\) , \( -16 a + 112\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-8a+56\right){x}-16a+112$ |
| 14.1-i1 |
14.1-i |
$2$ |
$3$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{18} \cdot 7^{3} \) |
$2.24040$ |
$(2,a), (a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$2.052397443$ |
2.850226208 |
\( \frac{9930171131}{392} a - \frac{9193553137}{56} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -36 a - 225\) , \( -2932 a - 18983\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-36a-225\right){x}-2932a-18983$ |
| 14.1-i2 |
14.1-i |
$2$ |
$3$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{14} \cdot 7 \) |
$2.24040$ |
$(2,a), (a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$18.47157698$ |
2.850226208 |
\( \frac{225}{14} a - \frac{169}{2} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 4 a + 35\) , \( 116 a + 773\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(4a+35\right){x}+116a+773$ |
| 14.1-j1 |
14.1-j |
$6$ |
$18$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{36} \cdot 7^{2} \) |
$2.24040$ |
$(2,a), (a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$26.30318993$ |
$0.436190660$ |
1.770354089 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-171{x}-874$ |
| 14.1-j2 |
14.1-j |
$6$ |
$18$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{4} \cdot 7^{2} \) |
$2.24040$ |
$(2,a), (a+7)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$2.922576659$ |
$35.33144352$ |
1.770354089 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}$ |
| 14.1-j3 |
14.1-j |
$6$ |
$18$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{12} \cdot 7^{6} \) |
$2.24040$ |
$(2,a), (a+7)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$8.767729977$ |
$3.925715946$ |
1.770354089 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+4{x}-6$ |
| 14.1-j4 |
14.1-j |
$6$ |
$18$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{6} \cdot 7^{12} \) |
$2.24040$ |
$(2,a), (a+7)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$4.383864988$ |
$3.925715946$ |
1.770354089 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-36{x}-70$ |
| 14.1-j5 |
14.1-j |
$6$ |
$18$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{2} \cdot 7^{4} \) |
$2.24040$ |
$(2,a), (a+7)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \) |
$1.461288329$ |
$35.33144352$ |
1.770354089 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-11{x}+12$ |
| 14.1-j6 |
14.1-j |
$6$ |
$18$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{18} \cdot 7^{4} \) |
$2.24040$ |
$(2,a), (a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$13.15159496$ |
$0.436190660$ |
1.770354089 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2731{x}-55146$ |
| 14.1-k1 |
14.1-k |
$6$ |
$18$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{48} \cdot 7^{2} \) |
$2.24040$ |
$(2,a), (a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$0.436190660$ |
5.451760094 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -23905663 a - 154926339\) , \( -162458649312 a - 1052852380264\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-23905663a-154926339\right){x}-162458649312a-1052852380264$ |
| 14.1-k2 |
14.1-k |
$6$ |
$18$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{16} \cdot 7^{2} \) |
$2.24040$ |
$(2,a), (a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$35.33144352$ |
5.451760094 |
\( -\frac{15625}{28} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -73023 a - 473179\) , \( 55263928 a + 358151328\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-73023a-473179\right){x}+55263928a+358151328$ |
| 14.1-k3 |
14.1-k |
$6$ |
$18$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{24} \cdot 7^{6} \) |
$2.24040$ |
$(2,a), (a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$3.925715946$ |
5.451760094 |
\( \frac{9938375}{21952} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 627937 a + 4069561\) , \( -1156642012 a - 7495896820\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(627937a+4069561\right){x}-1156642012a-7495896820$ |
| 14.1-k4 |
14.1-k |
$6$ |
$18$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{18} \cdot 7^{12} \) |
$2.24040$ |
$(2,a), (a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$3.925715946$ |
5.451760094 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -4979743 a - 32272359\) , \( -12626975292 a - 81832152532\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4979743a-32272359\right){x}-12626975292a-81832152532$ |
| 14.1-k5 |
14.1-k |
$6$ |
$18$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{14} \cdot 7^{4} \) |
$2.24040$ |
$(2,a), (a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$35.33144352$ |
5.451760094 |
\( \frac{128787625}{98} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -1474943 a - 9558659\) , \( 2479075808 a + 16066247624\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1474943a-9558659\right){x}+2479075808a+16066247624$ |
| 14.1-k6 |
14.1-k |
$6$ |
$18$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{30} \cdot 7^{4} \) |
$2.24040$ |
$(2,a), (a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$0.436190660$ |
5.451760094 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -382797183 a - 2480809219\) , \( -10378740177632 a - 67261923867240\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-382797183a-2480809219\right){x}-10378740177632a-67261923867240$ |
| 14.1-l1 |
14.1-l |
$2$ |
$3$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{6} \cdot 7^{3} \) |
$2.24040$ |
$(2,a), (a+7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$1.618106300$ |
$2.052397443$ |
3.074645990 |
\( \frac{9930171131}{392} a - \frac{9193553137}{56} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -9 a - 59\) , \( -353 a - 2288\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-9a-59\right){x}-353a-2288$ |
| 14.1-l2 |
14.1-l |
$2$ |
$3$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{2} \cdot 7 \) |
$2.24040$ |
$(2,a), (a+7)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$4.854318900$ |
$18.47157698$ |
3.074645990 |
\( \frac{225}{14} a - \frac{169}{2} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( a + 6\) , \( 13 a + 84\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+6\right){x}+13a+84$ |
*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.
