| 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 |
| 42.1-a1 |
42.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( 2^{16} \cdot 3^{4} \cdot 7^{2} \) |
$2.94853$ |
$(2,a), (3,a), (a+7)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$2.939829900$ |
$12.07873502$ |
5.479223448 |
\( -\frac{7189057}{16128} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -4\) , \( 5\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-4{x}+5$ |
| 42.1-a2 |
42.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( 2^{2} \cdot 3^{32} \cdot 7^{4} \) |
$2.94853$ |
$(2,a), (3,a), (a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$23.51863920$ |
$0.754920939$ |
5.479223448 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 386\) , \( 1277\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+386{x}+1277$ |
| 42.1-a3 |
42.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$2.94853$ |
$(2,a), (3,a), (a+7)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$11.75931960$ |
$3.019683757$ |
5.479223448 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-104{x}+101$ |
| 42.1-a4 |
42.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( 2^{2} \cdot 3^{8} \cdot 7^{16} \) |
$2.94853$ |
$(2,a), (3,a), (a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$23.51863920$ |
$0.754920939$ |
5.479223448 |
\( \frac{84448510979617}{933897762} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -914\) , \( -10915\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-914{x}-10915$ |
| 42.1-a5 |
42.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( 2^{8} \cdot 3^{8} \cdot 7^{4} \) |
$2.94853$ |
$(2,a), (3,a), (a+7)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$5.879659800$ |
$12.07873502$ |
5.479223448 |
\( \frac{65597103937}{63504} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -84\) , \( 261\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-84{x}+261$ |
| 42.1-a6 |
42.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( 2^{4} \cdot 3^{4} \cdot 7^{2} \) |
$2.94853$ |
$(2,a), (3,a), (a+7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$2.939829900$ |
$12.07873502$ |
5.479223448 |
\( \frac{268498407453697}{252} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -1344\) , \( 18405\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-1344{x}+18405$ |
| 42.1-b1 |
42.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( - 2^{17} \cdot 3^{5} \cdot 7 \) |
$2.94853$ |
$(2,a), (3,a), (a+7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1.554020442$ |
$12.25429810$ |
2.938465007 |
\( \frac{11417185093}{96768} a + \frac{880854947}{1152} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( -14 a - 87\) , \( 63 a + 399\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-14a-87\right){x}+63a+399$ |
| 42.1-c1 |
42.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( - 2^{17} \cdot 3^{5} \cdot 7 \) |
$2.94853$ |
$(2,a), (3,a), (a+7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1.554020442$ |
$12.25429810$ |
2.938465007 |
\( -\frac{11417185093}{96768} a + \frac{880854947}{1152} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -1082 a - 6989\) , \( 27258367 a + 176654415\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1082a-6989\right){x}+27258367a+176654415$ |
| 42.1-d1 |
42.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( - 2^{29} \cdot 3^{5} \cdot 7 \) |
$2.94853$ |
$(2,a), (3,a), (a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 17 \) |
$1$ |
$3.103902381$ |
4.071011550 |
\( \frac{11417185093}{96768} a + \frac{880854947}{1152} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 2\) , \( 12484 a - 80906\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+2{x}+12484a-80906$ |
| 42.1-e1 |
42.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( 2^{28} \cdot 3^{4} \cdot 7^{2} \) |
$2.94853$ |
$(2,a), (3,a), (a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$2.486887276$ |
1.534940151 |
\( -\frac{7189057}{16128} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -830 a - 5376\) , \( -78456 a - 508452\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-830a-5376\right){x}-78456a-508452$ |
| 42.1-e2 |
42.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( 2^{14} \cdot 3^{32} \cdot 7^{4} \) |
$2.94853$ |
$(2,a), (3,a), (a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{3} \) |
$1$ |
$0.621721819$ |
1.534940151 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 80290 a + 520344\) , \( -11628936 a - 75364116\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(80290a+520344\right){x}-11628936a-75364116$ |
| 42.1-e3 |
42.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( 2^{16} \cdot 3^{16} \cdot 7^{8} \) |
$2.94853$ |
$(2,a), (3,a), (a+7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{3} \) |
$1$ |
$2.486887276$ |
1.534940151 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -21630 a - 140176\) , \( -1676056 a - 10862084\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-21630a-140176\right){x}-1676056a-10862084$ |
| 42.1-e4 |
42.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( 2^{14} \cdot 3^{8} \cdot 7^{16} \) |
$2.94853$ |
$(2,a), (3,a), (a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$2.486887276$ |
1.534940151 |
\( \frac{84448510979617}{933897762} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -190110 a - 1232056\) , \( 112754264 a + 730731148\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-190110a-1232056\right){x}+112754264a+730731148$ |
| 42.1-e5 |
42.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( 2^{20} \cdot 3^{8} \cdot 7^{4} \) |
$2.94853$ |
$(2,a), (3,a), (a+7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{3} \) |
$1$ |
$2.486887276$ |
1.534940151 |
\( \frac{65597103937}{63504} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -17470 a - 113216\) , \( -3291896 a - 21333924\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-17470a-113216\right){x}-3291896a-21333924$ |
| 42.1-e6 |
42.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( 2^{16} \cdot 3^{4} \cdot 7^{2} \) |
$2.94853$ |
$(2,a), (3,a), (a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{3} \) |
$1$ |
$0.621721819$ |
1.534940151 |
\( \frac{268498407453697}{252} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -279550 a - 1811696\) , \( -206313176 a - 1337062212\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-279550a-1811696\right){x}-206313176a-1337062212$ |
| 42.1-f1 |
42.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( - 2^{29} \cdot 3^{5} \cdot 7 \) |
$2.94853$ |
$(2,a), (3,a), (a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 17 \) |
$1$ |
$3.103902381$ |
4.071011550 |
\( -\frac{11417185093}{96768} a + \frac{880854947}{1152} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 2\) , \( -12484 a - 80906\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+2{x}-12484a-80906$ |
| 42.1-g1 |
42.1-g |
$1$ |
$1$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( - 2^{17} \cdot 3^{5} \cdot 7 \) |
$2.94853$ |
$(2,a), (3,a), (a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \) |
$1$ |
$3.103902381$ |
1.197356338 |
\( -\frac{11417185093}{96768} a + \frac{880854947}{1152} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( a + 10\) , \( -1559 a - 10096\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+10\right){x}-1559a-10096$ |
| 42.1-h1 |
42.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( 2^{16} \cdot 3^{4} \cdot 7^{2} \) |
$2.94853$ |
$(2,a), (3,a), (a+7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1$ |
$2.486887276$ |
1.534940151 |
\( -\frac{7189057}{16128} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( 205 a - 1334\) , \( 10220 a - 66228\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(205a-1334\right){x}+10220a-66228$ |
| 42.1-h2 |
42.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( 2^{2} \cdot 3^{32} \cdot 7^{4} \) |
$2.94853$ |
$(2,a), (3,a), (a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1$ |
$0.621721819$ |
1.534940151 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( -20075 a + 130096\) , \( 1413470 a - 9160326\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-20075a+130096\right){x}+1413470a-9160326$ |
| 42.1-h3 |
42.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$2.94853$ |
$(2,a), (3,a), (a+7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$2.486887276$ |
1.534940151 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( 5405 a - 35034\) , \( 220320 a - 1427832\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(5405a-35034\right){x}+220320a-1427832$ |
| 42.1-h4 |
42.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( 2^{2} \cdot 3^{8} \cdot 7^{16} \) |
$2.94853$ |
$(2,a), (3,a), (a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$2.486887276$ |
1.534940151 |
\( \frac{84448510979617}{933897762} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( 47525 a - 308004\) , \( -13999230 a + 90725382\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(47525a-308004\right){x}-13999230a+90725382$ |
| 42.1-h5 |
42.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( 2^{8} \cdot 3^{8} \cdot 7^{4} \) |
$2.94853$ |
$(2,a), (3,a), (a+7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$2.486887276$ |
1.534940151 |
\( \frac{65597103937}{63504} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( 4365 a - 28294\) , \( 420220 a - 2723332\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(4365a-28294\right){x}+420220a-2723332$ |
| 42.1-h6 |
42.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( 2^{4} \cdot 3^{4} \cdot 7^{2} \) |
$2.94853$ |
$(2,a), (3,a), (a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$1$ |
$0.621721819$ |
1.534940151 |
\( \frac{268498407453697}{252} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( 69885 a - 452914\) , \( 25928920 a - 168038608\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(69885a-452914\right){x}+25928920a-168038608$ |
| 42.1-i1 |
42.1-i |
$1$ |
$1$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( - 2^{17} \cdot 3^{5} \cdot 7 \) |
$2.94853$ |
$(2,a), (3,a), (a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \) |
$1$ |
$3.103902381$ |
1.197356338 |
\( \frac{11417185093}{96768} a + \frac{880854947}{1152} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -9098 a - 58958\) , \( -1244792 a - 8067166\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-9098a-58958\right){x}-1244792a-8067166$ |
| 42.1-j1 |
42.1-j |
$1$ |
$1$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( - 2^{29} \cdot 3^{5} \cdot 7 \) |
$2.94853$ |
$(2,a), (3,a), (a+7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \cdot 17 \) |
$0.051919426$ |
$12.25429810$ |
8.344736084 |
\( -\frac{11417185093}{96768} a + \frac{880854947}{1152} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 54 a - 327\) , \( -342 a + 2271\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(54a-327\right){x}-342a+2271$ |
| 42.1-k1 |
42.1-k |
$1$ |
$1$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( - 2^{29} \cdot 3^{5} \cdot 7 \) |
$2.94853$ |
$(2,a), (3,a), (a+7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \cdot 17 \) |
$0.051919426$ |
$12.25429810$ |
8.344736084 |
\( \frac{11417185093}{96768} a + \frac{880854947}{1152} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -54 a - 327\) , \( 342 a + 2271\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-54a-327\right){x}+342a+2271$ |
| 42.1-l1 |
42.1-l |
$6$ |
$8$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( 2^{28} \cdot 3^{4} \cdot 7^{2} \) |
$2.94853$ |
$(2,a), (3,a), (a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.553231005$ |
$12.07873502$ |
4.124424068 |
\( -\frac{7189057}{16128} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 7\) , \( 39\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+7{x}+39$ |
| 42.1-l2 |
42.1-l |
$6$ |
$8$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( 2^{14} \cdot 3^{32} \cdot 7^{4} \) |
$2.94853$ |
$(2,a), (3,a), (a+7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$4.425848046$ |
$0.754920939$ |
4.124424068 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 1567\) , \( 14895\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+1567{x}+14895$ |
| 42.1-l3 |
42.1-l |
$6$ |
$8$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( 2^{16} \cdot 3^{16} \cdot 7^{8} \) |
$2.94853$ |
$(2,a), (3,a), (a+7)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$2.212924023$ |
$3.019683757$ |
4.124424068 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -393\) , \( -393\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-393{x}-393$ |
| 42.1-l4 |
42.1-l |
$6$ |
$8$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( 2^{14} \cdot 3^{8} \cdot 7^{16} \) |
$2.94853$ |
$(2,a), (3,a), (a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$4.425848046$ |
$0.754920939$ |
4.124424068 |
\( \frac{84448510979617}{933897762} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -3633\) , \( -98241\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-3633{x}-98241$ |
| 42.1-l5 |
42.1-l |
$6$ |
$8$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( 2^{20} \cdot 3^{8} \cdot 7^{4} \) |
$2.94853$ |
$(2,a), (3,a), (a+7)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.106462011$ |
$12.07873502$ |
4.124424068 |
\( \frac{65597103937}{63504} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -313\) , \( 1127\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-313{x}+1127$ |
| 42.1-l6 |
42.1-l |
$6$ |
$8$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
42.1 |
\( 2 \cdot 3 \cdot 7 \) |
\( 2^{16} \cdot 3^{4} \cdot 7^{2} \) |
$2.94853$ |
$(2,a), (3,a), (a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.553231005$ |
$12.07873502$ |
4.124424068 |
\( \frac{268498407453697}{252} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -5353\) , \( 131159\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-5353{x}+131159$ |
*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.
