| Label |
Cremona label |
Class |
Cremona class |
Class size |
Class degree |
Conductor |
Discriminant |
Rank |
Torsion |
$\textrm{End}^0(E_{\overline\Q})$ |
CM |
Sato-Tate |
Semistable |
Potentially good |
Nonmax $\ell$ |
$\ell$-adic images |
mod-$\ell$ images |
Adelic level |
Adelic index |
Adelic genus |
Regulator |
$Ш_{\textrm{an}}$ |
Ш primes |
Integral points |
Modular degree |
Faltings height |
j-invariant |
$abc$ quality |
Szpiro ratio |
Weierstrass coefficients |
Weierstrass equation |
mod-$m$ images |
MW-generators |
| 33327.a1 |
33327l1 |
33327.a |
33327l |
$1$ |
$1$ |
\( 3^{2} \cdot 7 \cdot 23^{2} \) |
\( - 3^{7} \cdot 7 \cdot 23^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$966$ |
$2$ |
$0$ |
$0.893302331$ |
$1$ |
|
$4$ |
$84480$ |
$1.319223$ |
$512000/483$ |
$0.74348$ |
$3.70177$ |
$[0, 0, 1, 7935, 215964]$ |
\(y^2+y=x^3+7935x+215964\) |
966.2.0.? |
$[(161, 2380)]$ |
| 33327.b1 |
33327d1 |
33327.b |
33327d |
$1$ |
$1$ |
\( 3^{2} \cdot 7 \cdot 23^{2} \) |
\( - 3^{3} \cdot 7^{7} \cdot 23^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$966$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$413952$ |
$1.984154$ |
$-226534772736/18941489$ |
$0.99435$ |
$4.64657$ |
$[0, 0, 1, -201549, -37258396]$ |
\(y^2+y=x^3-201549x-37258396\) |
966.2.0.? |
$[]$ |
| 33327.c1 |
33327r1 |
33327.c |
33327r |
$1$ |
$1$ |
\( 3^{2} \cdot 7 \cdot 23^{2} \) |
\( - 3^{11} \cdot 7 \cdot 23^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$966$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1267200$ |
$2.242573$ |
$-98867482624/20696067$ |
$1.05025$ |
$4.90012$ |
$[0, 0, 1, -458643, -139509864]$ |
\(y^2+y=x^3-458643x-139509864\) |
966.2.0.? |
$[]$ |
| 33327.d1 |
33327p1 |
33327.d |
33327p |
$1$ |
$1$ |
\( 3^{2} \cdot 7 \cdot 23^{2} \) |
\( 3^{7} \cdot 7^{3} \cdot 23^{2} \) |
$2$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$42$ |
$2$ |
$0$ |
$0.239505044$ |
$1$ |
|
$18$ |
$13824$ |
$0.486508$ |
$160261033/1029$ |
$0.87602$ |
$3.04922$ |
$[1, -1, 1, -824, 9254]$ |
\(y^2+xy+y=x^3-x^2-824x+9254\) |
42.2.0.a.1 |
$[(12, 25), (-9, 130)]$ |
| 33327.e1 |
33327f1 |
33327.e |
33327f |
$1$ |
$1$ |
\( 3^{2} \cdot 7 \cdot 23^{2} \) |
\( 3^{9} \cdot 7 \cdot 23^{4} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$42$ |
$2$ |
$0$ |
$0.388037924$ |
$1$ |
|
$6$ |
$18432$ |
$0.724568$ |
$14283/7$ |
$0.91239$ |
$3.07240$ |
$[1, -1, 1, -893, 4240]$ |
\(y^2+xy+y=x^3-x^2-893x+4240\) |
42.2.0.a.1 |
$[(52, 284)]$ |
| 33327.f1 |
33327i2 |
33327.f |
33327i |
$2$ |
$2$ |
\( 3^{2} \cdot 7 \cdot 23^{2} \) |
\( 3^{10} \cdot 7^{8} \cdot 23^{3} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.128 |
2B |
$7728$ |
$192$ |
$9$ |
$3.634851230$ |
$1$ |
|
$4$ |
$135168$ |
$1.741724$ |
$6163717745375/466948881$ |
$0.98902$ |
$4.36406$ |
$[1, -1, 1, -79070, 7997798]$ |
\(y^2+xy+y=x^3-x^2-79070x+7997798\) |
2.3.0.a.1, 4.6.0.e.1, 8.24.0.bi.1, 48.48.1.fo.1, 92.12.0.?, $\ldots$ |
$[(121, 376)]$ |
| 33327.f2 |
33327i1 |
33327.f |
33327i |
$2$ |
$2$ |
\( 3^{2} \cdot 7 \cdot 23^{2} \) |
\( - 3^{14} \cdot 7^{4} \cdot 23^{3} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.83 |
2B |
$7728$ |
$192$ |
$9$ |
$1.817425615$ |
$1$ |
|
$7$ |
$67584$ |
$1.395151$ |
$1349232625/15752961$ |
$0.98873$ |
$3.83850$ |
$[1, -1, 1, 4765, 553250]$ |
\(y^2+xy+y=x^3-x^2+4765x+553250\) |
2.3.0.a.1, 4.12.0.f.1, 8.24.0.bt.1, 46.6.0.a.1, 48.48.1.fv.1, $\ldots$ |
$[(-60, 250)]$ |
| 33327.g1 |
33327o2 |
33327.g |
33327o |
$2$ |
$2$ |
\( 3^{2} \cdot 7 \cdot 23^{2} \) |
\( 3^{10} \cdot 7^{8} \cdot 23^{9} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.128 |
2B |
$7728$ |
$192$ |
$9$ |
$1$ |
$1$ |
|
$0$ |
$3108864$ |
$3.309471$ |
$6163717745375/466948881$ |
$0.98902$ |
$6.17055$ |
$[1, -1, 1, -41827865, -97058244310]$ |
\(y^2+xy+y=x^3-x^2-41827865x-97058244310\) |
2.3.0.a.1, 4.6.0.e.1, 8.24.0.bi.1, 48.48.1.fo.1, 92.12.0.?, $\ldots$ |
$[]$ |
| 33327.g2 |
33327o1 |
33327.g |
33327o |
$2$ |
$2$ |
\( 3^{2} \cdot 7 \cdot 23^{2} \) |
\( - 3^{14} \cdot 7^{4} \cdot 23^{9} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.83 |
2B |
$7728$ |
$192$ |
$9$ |
$1$ |
$1$ |
|
$1$ |
$1554432$ |
$2.962898$ |
$1349232625/15752961$ |
$0.98873$ |
$5.64498$ |
$[1, -1, 1, 2520850, -6746521084]$ |
\(y^2+xy+y=x^3-x^2+2520850x-6746521084\) |
2.3.0.a.1, 4.12.0.f.1, 8.24.0.bt.1, 46.6.0.a.1, 48.48.1.fv.1, $\ldots$ |
$[]$ |
| 33327.h1 |
33327b1 |
33327.h |
33327b |
$1$ |
$1$ |
\( 3^{2} \cdot 7 \cdot 23^{2} \) |
\( 3^{9} \cdot 7 \cdot 23^{10} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$42$ |
$2$ |
$0$ |
$1$ |
$4$ |
$2$ |
$0$ |
$423936$ |
$2.292316$ |
$14283/7$ |
$0.91239$ |
$4.87888$ |
$[1, -1, 1, -472232, -48757922]$ |
\(y^2+xy+y=x^3-x^2-472232x-48757922\) |
42.2.0.a.1 |
$[]$ |
| 33327.i1 |
33327j1 |
33327.i |
33327j |
$1$ |
$1$ |
\( 3^{2} \cdot 7 \cdot 23^{2} \) |
\( 3^{7} \cdot 7^{3} \cdot 23^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$42$ |
$2$ |
$0$ |
$5.853966225$ |
$1$ |
|
$2$ |
$317952$ |
$2.054256$ |
$160261033/1029$ |
$0.87602$ |
$4.85571$ |
$[1, -1, 1, -435731, -109982266]$ |
\(y^2+xy+y=x^3-x^2-435731x-109982266\) |
42.2.0.a.1 |
$[(996, 20557)]$ |
| 33327.j1 |
33327h1 |
33327.j |
33327h |
$1$ |
$1$ |
\( 3^{2} \cdot 7 \cdot 23^{2} \) |
\( - 3^{8} \cdot 7^{2} \cdot 23^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.2.0.1 |
|
$1288$ |
$4$ |
$0$ |
$1.453345646$ |
$1$ |
|
$2$ |
$10752$ |
$0.338117$ |
$-8231953/441$ |
$0.83649$ |
$2.77265$ |
$[1, -1, 0, -306, -2079]$ |
\(y^2+xy=x^3-x^2-306x-2079\) |
4.2.0.a.1, 1288.4.0.? |
$[(24, 51)]$ |
| 33327.k1 |
33327m6 |
33327.k |
33327m |
$6$ |
$8$ |
\( 3^{2} \cdot 7 \cdot 23^{2} \) |
\( 3^{7} \cdot 7^{2} \cdot 23^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.24.0.13 |
2B |
$7728$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$405504$ |
$2.191257$ |
$53297461115137/147$ |
$1.05087$ |
$5.47445$ |
$[1, -1, 0, -3732723, -2774857986]$ |
\(y^2+xy=x^3-x^2-3732723x-2774857986\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0.h.1, 16.24.0.e.2, $\ldots$ |
$[]$ |
| 33327.k2 |
33327m4 |
33327.k |
33327m |
$6$ |
$8$ |
\( 3^{2} \cdot 7 \cdot 23^{2} \) |
\( 3^{8} \cdot 7^{4} \cdot 23^{6} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.18 |
2Cs |
$3864$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$2$ |
$202752$ |
$1.844685$ |
$13027640977/21609$ |
$1.08149$ |
$4.67586$ |
$[1, -1, 0, -233388, -43277085]$ |
\(y^2+xy=x^3-x^2-233388x-43277085\) |
2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.1, 12.24.0.c.1, 24.48.0.j.2, $\ldots$ |
$[]$ |
| 33327.k3 |
33327m3 |
33327.k |
33327m |
$6$ |
$8$ |
\( 3^{2} \cdot 7 \cdot 23^{2} \) |
\( 3^{14} \cdot 7 \cdot 23^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.88 |
2B |
$7728$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$202752$ |
$1.844685$ |
$6570725617/45927$ |
$1.00160$ |
$4.61014$ |
$[1, -1, 0, -185778, 30680289]$ |
\(y^2+xy=x^3-x^2-185778x+30680289\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.1, 28.12.0.h.1, 48.48.0.bf.1, $\ldots$ |
$[]$ |
| 33327.k4 |
33327m5 |
33327.k |
33327m |
$6$ |
$8$ |
\( 3^{2} \cdot 7 \cdot 23^{2} \) |
\( - 3^{7} \cdot 7^{8} \cdot 23^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.90 |
2B |
$7728$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$405504$ |
$2.191257$ |
$-4354703137/17294403$ |
$1.04266$ |
$4.76865$ |
$[1, -1, 0, -161973, -70314804]$ |
\(y^2+xy=x^3-x^2-161973x-70314804\) |
2.3.0.a.1, 4.6.0.c.1, 6.6.0.a.1, 8.24.0.bb.2, 12.12.0.g.1, $\ldots$ |
$[]$ |
| 33327.k5 |
33327m2 |
33327.k |
33327m |
$6$ |
$8$ |
\( 3^{2} \cdot 7 \cdot 23^{2} \) |
\( 3^{10} \cdot 7^{2} \cdot 23^{6} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.10 |
2Cs |
$3864$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$2$ |
$101376$ |
$1.498112$ |
$7189057/3969$ |
$1.14862$ |
$3.95547$ |
$[1, -1, 0, -19143, -213840]$ |
\(y^2+xy=x^3-x^2-19143x-213840\) |
2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.2, 24.48.0.w.2, 28.24.0.c.1, $\ldots$ |
$[]$ |
| 33327.k6 |
33327m1 |
33327.k |
33327m |
$6$ |
$8$ |
\( 3^{2} \cdot 7 \cdot 23^{2} \) |
\( - 3^{8} \cdot 7 \cdot 23^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.24.0.1 |
2B |
$7728$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$50688$ |
$1.151537$ |
$103823/63$ |
$0.97868$ |
$3.54855$ |
$[1, -1, 0, 4662, -28161]$ |
\(y^2+xy=x^3-x^2+4662x-28161\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 14.6.0.b.1, 16.24.0.e.1, $\ldots$ |
$[]$ |
| 33327.l1 |
33327a1 |
33327.l |
33327a |
$1$ |
$1$ |
\( 3^{2} \cdot 7 \cdot 23^{2} \) |
\( 3^{3} \cdot 7 \cdot 23^{10} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$42$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$141312$ |
$1.743010$ |
$14283/7$ |
$0.91239$ |
$4.24593$ |
$[1, -1, 0, -52470, 1823339]$ |
\(y^2+xy=x^3-x^2-52470x+1823339\) |
42.2.0.a.1 |
$[]$ |
| 33327.m1 |
33327e1 |
33327.m |
33327e |
$1$ |
$1$ |
\( 3^{2} \cdot 7 \cdot 23^{2} \) |
\( 3^{3} \cdot 7 \cdot 23^{4} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$42$ |
$2$ |
$0$ |
$2.358523088$ |
$1$ |
|
$2$ |
$6144$ |
$0.175263$ |
$14283/7$ |
$0.91239$ |
$2.43944$ |
$[1, -1, 0, -99, -124]$ |
\(y^2+xy=x^3-x^2-99x-124\) |
42.2.0.a.1 |
$[(-4, 16)]$ |
| 33327.n1 |
33327g4 |
33327.n |
33327g |
$4$ |
$4$ |
\( 3^{2} \cdot 7 \cdot 23^{2} \) |
\( 3^{6} \cdot 7^{4} \cdot 23^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$3864$ |
$48$ |
$0$ |
$4.922305807$ |
$1$ |
|
$0$ |
$337920$ |
$2.011421$ |
$209267191953/55223$ |
$0.94092$ |
$4.94247$ |
$[1, -1, 0, -588876, 174041405]$ |
\(y^2+xy=x^3-x^2-588876x+174041405\) |
2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 56.12.0.z.1, 92.12.0.?, $\ldots$ |
$[(3293/4, 495435/4)]$ |
| 33327.n2 |
33327g2 |
33327.n |
33327g |
$4$ |
$4$ |
\( 3^{2} \cdot 7 \cdot 23^{2} \) |
\( 3^{6} \cdot 7^{2} \cdot 23^{8} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.6.0.1 |
2Cs |
$1932$ |
$48$ |
$0$ |
$9.844611614$ |
$1$ |
|
$2$ |
$168960$ |
$1.664846$ |
$72511713/25921$ |
$0.92625$ |
$4.17739$ |
$[1, -1, 0, -41361, 2012192]$ |
\(y^2+xy=x^3-x^2-41361x+2012192\) |
2.6.0.a.1, 12.12.0-2.a.1.1, 28.12.0.b.1, 84.24.0.?, 92.12.0.?, $\ldots$ |
$[(-86741/22, 21281731/22)]$ |
| 33327.n3 |
33327g1 |
33327.n |
33327g |
$4$ |
$4$ |
\( 3^{2} \cdot 7 \cdot 23^{2} \) |
\( 3^{6} \cdot 7 \cdot 23^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$3864$ |
$48$ |
$0$ |
$19.68922322$ |
$1$ |
|
$1$ |
$84480$ |
$1.318272$ |
$5545233/161$ |
$0.79467$ |
$3.93054$ |
$[1, -1, 0, -17556, -868213]$ |
\(y^2+xy=x^3-x^2-17556x-868213\) |
2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 56.12.0.z.1, 168.24.0.?, $\ldots$ |
$[(-411703159/2288, 2223868405901/2288)]$ |
| 33327.n4 |
33327g3 |
33327.n |
33327g |
$4$ |
$4$ |
\( 3^{2} \cdot 7 \cdot 23^{2} \) |
\( - 3^{6} \cdot 7 \cdot 23^{10} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$3864$ |
$48$ |
$0$ |
$19.68922322$ |
$1$ |
|
$0$ |
$337920$ |
$2.011421$ |
$2014698447/1958887$ |
$0.97932$ |
$4.49662$ |
$[1, -1, 0, 125274, 14043239]$ |
\(y^2+xy=x^3-x^2+125274x+14043239\) |
2.3.0.a.1, 4.6.0.c.1, 14.6.0.b.1, 24.12.0-4.c.1.3, 28.12.0.g.1, $\ldots$ |
$[(-90478517/1606, 12910022684731/1606)]$ |
| 33327.o1 |
33327n1 |
33327.o |
33327n |
$1$ |
$1$ |
\( 3^{2} \cdot 7 \cdot 23^{2} \) |
\( - 3^{8} \cdot 7^{2} \cdot 23^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.2.0.1 |
|
$56$ |
$4$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$247296$ |
$1.905865$ |
$-8231953/441$ |
$0.83649$ |
$4.57914$ |
$[1, -1, 0, -161973, 26266842]$ |
\(y^2+xy=x^3-x^2-161973x+26266842\) |
4.2.0.a.1, 56.4.0-4.a.1.1 |
$[]$ |
| 33327.p1 |
33327c1 |
33327.p |
33327c |
$1$ |
$1$ |
\( 3^{2} \cdot 7 \cdot 23^{2} \) |
\( - 3^{9} \cdot 7^{7} \cdot 23^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$966$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1241856$ |
$2.533463$ |
$-226534772736/18941489$ |
$0.99435$ |
$5.27952$ |
$[0, 0, 1, -1813941, 1005976685]$ |
\(y^2+y=x^3-1813941x+1005976685\) |
966.2.0.? |
$[]$ |
| 33327.q1 |
33327q1 |
33327.q |
33327q |
$1$ |
$1$ |
\( 3^{2} \cdot 7 \cdot 23^{2} \) |
\( - 3^{13} \cdot 7^{3} \cdot 23^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$966$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$80640$ |
$1.148369$ |
$929714176/750141$ |
$0.97832$ |
$3.51912$ |
$[0, 0, 1, 4209, -65993]$ |
\(y^2+y=x^3+4209x-65993\) |
966.2.0.? |
$[]$ |
| 33327.r1 |
33327k1 |
33327.r |
33327k |
$1$ |
$1$ |
\( 3^{2} \cdot 7 \cdot 23^{2} \) |
\( - 3^{13} \cdot 7^{3} \cdot 23^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$966$ |
$2$ |
$0$ |
$30.61163026$ |
$1$ |
|
$0$ |
$1854720$ |
$2.716114$ |
$929714176/750141$ |
$0.97832$ |
$5.32561$ |
$[0, 0, 1, 2226561, 802933789]$ |
\(y^2+y=x^3+2226561x+802933789\) |
966.2.0.? |
$[(-801844895095079/1991068, 146460017392250592783037/1991068)]$ |
