| 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 |
| 39204.6-a1 |
39204.6-a |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39204.6 |
\( 2^{2} \cdot 3^{4} \cdot 11^{2} \) |
\( 2^{23} \cdot 3^{16} \cdot 11^{3} \) |
$3.32675$ |
$(a), (-a+1), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.805513358$ |
$0.459518212$ |
2.238445055 |
\( \frac{20138209}{49152} a - \frac{111021713}{147456} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -57 a + 180\) , \( -1003 a - 138\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-57a+180\right){x}-1003a-138$ |
| 39204.6-a2 |
39204.6-a |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39204.6 |
\( 2^{2} \cdot 3^{4} \cdot 11^{2} \) |
\( 2^{25} \cdot 3^{14} \cdot 11^{3} \) |
$3.32675$ |
$(a), (-a+1), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.611026716$ |
$0.459518212$ |
2.238445055 |
\( -\frac{1217204443}{262144} a + \frac{470888579}{393216} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 21 a + 285\) , \( -1553 a + 731\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(21a+285\right){x}-1553a+731$ |
| 39204.6-b1 |
39204.6-b |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39204.6 |
\( 2^{2} \cdot 3^{4} \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{16} \cdot 11^{9} \) |
$3.32675$ |
$(a), (-a+1), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.245782654$ |
2.229530679 |
\( -\frac{11528611}{576} a - \frac{43599055}{288} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 1144 a - 1818\) , \( 24339 a - 20058\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(1144a-1818\right){x}+24339a-20058$ |
| 39204.6-b2 |
39204.6-b |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39204.6 |
\( 2^{2} \cdot 3^{4} \cdot 11^{2} \) |
\( 2^{7} \cdot 3^{20} \cdot 11^{9} \) |
$3.32675$ |
$(a), (-a+1), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.245782654$ |
2.229530679 |
\( -\frac{45799}{1296} a + \frac{731363}{1296} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -2 a - 543\) , \( 5406 a - 3053\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-2a-543\right){x}+5406a-3053$ |
| 39204.6-c1 |
39204.6-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39204.6 |
\( 2^{2} \cdot 3^{4} \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{20} \cdot 11^{14} \) |
$3.32675$ |
$(a), (-a+1), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 5 \) |
$2.701373009$ |
$0.084272187$ |
6.883507518 |
\( \frac{34147229879407}{61735357728} a + \frac{275344585935545}{277809109776} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -2309 a + 6603\) , \( 110874 a - 62365\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-2309a+6603\right){x}+110874a-62365$ |
| 39204.6-c2 |
39204.6-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39204.6 |
\( 2^{2} \cdot 3^{4} \cdot 11^{2} \) |
\( 2^{23} \cdot 3^{14} \cdot 11^{8} \) |
$3.32675$ |
$(a), (-a+1), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \cdot 5 \) |
$0.675343252$ |
$0.168544375$ |
6.883507518 |
\( \frac{11336952210079}{380633088} a + \frac{71100053329}{63438848} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 2353 a - 108\) , \( 15977 a + 60494\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(2353a-108\right){x}+15977a+60494$ |
| 39204.6-c3 |
39204.6-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39204.6 |
\( 2^{2} \cdot 3^{4} \cdot 11^{2} \) |
\( 2^{16} \cdot 3^{16} \cdot 11^{10} \) |
$3.32675$ |
$(a), (-a+1), (2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \cdot 5 \) |
$1.350686504$ |
$0.168544375$ |
6.883507518 |
\( -\frac{102397297499}{134931456} a + \frac{150774304457}{67465728} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 931 a - 1677\) , \( 14178 a - 4981\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(931a-1677\right){x}+14178a-4981$ |
| 39204.6-c4 |
39204.6-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39204.6 |
\( 2^{2} \cdot 3^{4} \cdot 11^{2} \) |
\( 2^{17} \cdot 3^{14} \cdot 11^{8} \) |
$3.32675$ |
$(a), (-a+1), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$2.701373009$ |
$0.168544375$ |
6.883507518 |
\( -\frac{2553161206303}{1486848} a + \frac{335587165399}{495616} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -2435 a - 4086\) , \( 104411 a + 77706\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-2435a-4086\right){x}+104411a+77706$ |
| 39204.6-d1 |
39204.6-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39204.6 |
\( 2^{2} \cdot 3^{4} \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{20} \cdot 11^{6} \) |
$3.32675$ |
$(a), (-a+1), (2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1.150277665$ |
$0.427235553$ |
5.943893680 |
\( \frac{4913}{1296} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -26 a + 22\) , \( -1195 a - 23\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-26a+22\right){x}-1195a-23$ |
| 39204.6-d2 |
39204.6-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39204.6 |
\( 2^{2} \cdot 3^{4} \cdot 11^{2} \) |
\( 2^{17} \cdot 3^{14} \cdot 11^{6} \) |
$3.32675$ |
$(a), (-a+1), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1.150277665$ |
$0.427235553$ |
5.943893680 |
\( \frac{43993943}{196608} a + \frac{189091403}{98304} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -8 a - 266\) , \( -209 a - 553\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-8a-266\right){x}-209a-553$ |
| 39204.6-d3 |
39204.6-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39204.6 |
\( 2^{2} \cdot 3^{4} \cdot 11^{2} \) |
\( 2^{17} \cdot 3^{14} \cdot 11^{6} \) |
$3.32675$ |
$(a), (-a+1), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$0.287569416$ |
$0.427235553$ |
5.943893680 |
\( -\frac{43993943}{196608} a + \frac{140725583}{65536} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 100 a + 184\) , \( -551 a + 563\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(100a+184\right){x}-551a+563$ |
| 39204.6-d4 |
39204.6-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39204.6 |
\( 2^{2} \cdot 3^{4} \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{28} \cdot 11^{6} \) |
$3.32675$ |
$(a), (-a+1), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$2.300555330$ |
$0.213617776$ |
5.943893680 |
\( \frac{838561807}{26244} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 1414 a - 1238\) , \( -22975 a - 23\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(1414a-1238\right){x}-22975a-23$ |
| 39204.6-d5 |
39204.6-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39204.6 |
\( 2^{2} \cdot 3^{4} \cdot 11^{2} \) |
\( 2^{10} \cdot 3^{16} \cdot 11^{6} \) |
$3.32675$ |
$(a), (-a+1), (2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$0.575138832$ |
$0.427235553$ |
5.943893680 |
\( \frac{56620795}{2304} a + \frac{115022599}{2304} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -308 a + 541\) , \( -1282 a - 4197\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-308a+541\right){x}-1282a-4197$ |
| 39204.6-d6 |
39204.6-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39204.6 |
\( 2^{2} \cdot 3^{4} \cdot 11^{2} \) |
\( 2^{10} \cdot 3^{16} \cdot 11^{6} \) |
$3.32675$ |
$(a), (-a+1), (2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$2.300555330$ |
$0.427235553$ |
5.943893680 |
\( -\frac{56620795}{2304} a + \frac{85821697}{1152} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -416 a + 91\) , \( -3320 a + 3969\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-416a+91\right){x}-3320a+3969$ |
| 39204.6-d7 |
39204.6-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39204.6 |
\( 2^{2} \cdot 3^{4} \cdot 11^{2} \) |
\( 2^{5} \cdot 3^{14} \cdot 11^{6} \) |
$3.32675$ |
$(a), (-a+1), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1.150277665$ |
$0.213617776$ |
5.943893680 |
\( \frac{145011769343}{48} a + \frac{19365113857}{16} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -4898 a + 8641\) , \( -85468 a - 264585\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-4898a+8641\right){x}-85468a-264585$ |
| 39204.6-d8 |
39204.6-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39204.6 |
\( 2^{2} \cdot 3^{4} \cdot 11^{2} \) |
\( 2^{5} \cdot 3^{14} \cdot 11^{6} \) |
$3.32675$ |
$(a), (-a+1), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$4.601110661$ |
$0.213617776$ |
5.943893680 |
\( -\frac{145011769343}{48} a + \frac{101553555457}{24} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -6626 a + 1441\) , \( -218456 a + 257553\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-6626a+1441\right){x}-218456a+257553$ |
| 39204.6-e1 |
39204.6-e |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39204.6 |
\( 2^{2} \cdot 3^{4} \cdot 11^{2} \) |
\( 2^{7} \cdot 3^{16} \cdot 11^{7} \) |
$3.32675$ |
$(a), (-a+1), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.528361762$ |
4.792847404 |
\( \frac{1375753}{6336} a - \frac{1038611}{6336} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -72 a + 40\) , \( -54 a + 911\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-72a+40\right){x}-54a+911$ |
| 39204.6-e2 |
39204.6-e |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39204.6 |
\( 2^{2} \cdot 3^{4} \cdot 11^{2} \) |
\( 2^{5} \cdot 3^{14} \cdot 11^{8} \) |
$3.32675$ |
$(a), (-a+1), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.528361762$ |
4.792847404 |
\( -\frac{17031617}{2904} a + \frac{21786113}{2904} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -108 a + 253\) , \( 584 a + 867\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-108a+253\right){x}+584a+867$ |
*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.
