| 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 |
| 42592.6-a1 |
42592.6-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42592.6 |
\( 2^{5} \cdot 11^{3} \) |
\( 2^{22} \cdot 11^{9} \) |
$3.39641$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$4.108013610$ |
$0.253403434$ |
3.147642043 |
\( -\frac{2775668240489}{85184} a - \frac{5083125111585}{85184} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -2095 a - 2217\) , \( -70270 a - 16210\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-2095a-2217\right){x}-70270a-16210$ |
| 42592.6-a2 |
42592.6-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42592.6 |
\( 2^{5} \cdot 11^{3} \) |
\( 2^{19} \cdot 11^{18} \) |
$3.39641$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$4.108013610$ |
$0.126701717$ |
3.147642043 |
\( \frac{41728910180660407}{200859416110144} a - \frac{51818768961625453}{200859416110144} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 39 a - 1713\) , \( -20090 a - 50756\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(39a-1713\right){x}-20090a-50756$ |
| 42592.6-a3 |
42592.6-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42592.6 |
\( 2^{5} \cdot 11^{3} \) |
\( 2^{37} \cdot 11^{9} \) |
$3.39641$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$4.108013610$ |
$0.253403434$ |
3.147642043 |
\( \frac{74168468086089}{22330474496} a + \frac{16633019348749}{22330474496} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 584 a + 231\) , \( 581 a + 9461\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(584a+231\right){x}+581a+9461$ |
| 42592.6-a4 |
42592.6-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42592.6 |
\( 2^{5} \cdot 11^{3} \) |
\( 2^{26} \cdot 11^{7} \) |
$3.39641$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1.369337870$ |
$0.760210303$ |
3.147642043 |
\( -\frac{2222449}{45056} a + \frac{22133027}{22528} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -15 a - 57\) , \( -126 a + 190\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-15a-57\right){x}-126a+190$ |
| 42592.6-a5 |
42592.6-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42592.6 |
\( 2^{5} \cdot 11^{3} \) |
\( 2^{22} \cdot 11^{8} \) |
$3.39641$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{6} \) |
$0.684668935$ |
$0.760210303$ |
3.147642043 |
\( \frac{998361}{7744} a + \frac{11225095}{3872} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 69 a - 53\) , \( -140 a - 40\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(69a-53\right){x}-140a-40$ |
| 42592.6-a6 |
42592.6-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42592.6 |
\( 2^{5} \cdot 11^{3} \) |
\( 2^{26} \cdot 11^{12} \) |
$3.39641$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{6} \) |
$2.054006805$ |
$0.253403434$ |
3.147642043 |
\( -\frac{49453830610989}{7256313856} a + \frac{47470228116479}{7256313856} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -671 a + 947\) , \( -384 a - 12896\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-671a+947\right){x}-384a-12896$ |
| 42592.6-a7 |
42592.6-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42592.6 |
\( 2^{5} \cdot 11^{3} \) |
\( 2^{23} \cdot 11^{7} \) |
$3.39641$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1.369337870$ |
$0.760210303$ |
3.147642043 |
\( -\frac{7153263}{2816} a + \frac{88973461}{2816} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -6 a - 149\) , \( -31 a + 765\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-6a-149\right){x}-31a+765$ |
| 42592.6-a8 |
42592.6-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42592.6 |
\( 2^{5} \cdot 11^{3} \) |
\( 2^{17} \cdot 11^{10} \) |
$3.39641$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1.369337870$ |
$0.380105151$ |
3.147642043 |
\( \frac{67333244623}{117128} a + \frac{61299754338}{14641} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 989 a - 773\) , \( -12500 a - 2488\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(989a-773\right){x}-12500a-2488$ |
| 42592.6-b1 |
42592.6-b |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42592.6 |
\( 2^{5} \cdot 11^{3} \) |
\( 2^{17} \cdot 11^{5} \) |
$3.39641$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{3} \cdot 3 \) |
$0.037373195$ |
$1.936682811$ |
5.252558945 |
\( -\frac{173}{704} a + \frac{215}{352} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 1\) , \( a + 18\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+{x}+a+18$ |
| 42592.6-c1 |
42592.6-c |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42592.6 |
\( 2^{5} \cdot 11^{3} \) |
\( 2^{21} \cdot 11^{9} \) |
$3.39641$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$0.649149721$ |
1.962844260 |
\( \frac{399175}{1408} a + \frac{5454499}{1408} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -54 a - 89\) , \( -250 a - 123\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-54a-89\right){x}-250a-123$ |
| 42592.6-d1 |
42592.6-d |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42592.6 |
\( 2^{5} \cdot 11^{3} \) |
\( 2^{51} \cdot 11^{3} \) |
$3.39641$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{3} \cdot 3 \cdot 5 \) |
$0.103483218$ |
$0.399286256$ |
7.496292234 |
\( \frac{4070378798731}{11811160064} a + \frac{106097102447}{5905580032} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 148 a - 98\) , \( -1422 a + 1051\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(148a-98\right){x}-1422a+1051$ |
| 42592.6-d2 |
42592.6-d |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42592.6 |
\( 2^{5} \cdot 11^{3} \) |
\( 2^{25} \cdot 11^{5} \) |
$3.39641$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{3} \cdot 3 \cdot 5 \) |
$0.034494406$ |
$1.197858769$ |
7.496292234 |
\( -\frac{531165637}{1362944} a + \frac{64260511}{681472} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -17 a + 12\) , \( 52 a - 49\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-17a+12\right){x}+52a-49$ |
| 42592.6-e1 |
42592.6-e |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42592.6 |
\( 2^{5} \cdot 11^{3} \) |
\( 2^{7} \cdot 11^{8} \) |
$3.39641$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.516448036$ |
3.438980898 |
\( -\frac{1374871}{968} a - \frac{22437003}{484} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 22 a - 38\) , \( 61 a - 56\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(22a-38\right){x}+61a-56$ |
| 42592.6-e2 |
42592.6-e |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42592.6 |
\( 2^{5} \cdot 11^{3} \) |
\( 2^{13} \cdot 11^{12} \) |
$3.39641$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.505482678$ |
3.438980898 |
\( -\frac{2638880885903}{907039232} a - \frac{10019801056547}{453519616} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 227 a + 12\) , \( -435 a - 2172\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(227a+12\right){x}-435a-2172$ |
| 42592.6-e3 |
42592.6-e |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42592.6 |
\( 2^{5} \cdot 11^{3} \) |
\( 2^{14} \cdot 11^{7} \) |
$3.39641$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.516448036$ |
3.438980898 |
\( \frac{328039}{704} a + \frac{31003}{352} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 11 a - 8\) , \( 24 a - 29\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(11a-8\right){x}+24a-29$ |
| 42592.6-e4 |
42592.6-e |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42592.6 |
\( 2^{5} \cdot 11^{3} \) |
\( 2^{26} \cdot 11^{9} \) |
$3.39641$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.505482678$ |
3.438980898 |
\( -\frac{198874755649}{348913664} a + \frac{23956044435}{174456832} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -104 a + 82\) , \( -634 a + 991\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-104a+82\right){x}-634a+991$ |
*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.
