| 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 |
Intrinsic torsion order |
Weierstrass coefficients |
Weierstrass equation |
mod-$m$ images |
MW-generators |
Manin constant |
| 339762.a1 |
339762a1 |
339762.a |
339762a |
$2$ |
$2$ |
\( 2 \cdot 3 \cdot 17 \cdot 3331 \) |
\( 2^{22} \cdot 3 \cdot 17 \cdot 3331 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.4 |
2B |
$1359048$ |
$12$ |
$0$ |
$12.94463603$ |
$1$ |
|
$1$ |
$535744$ |
$0.981778$ |
$2577720940501897/712532557824$ |
$0.84525$ |
$2.78625$ |
$1$ |
$[1, 1, 0, -2856, 41280]$ |
\(y^2+xy=x^3+x^2-2856x+41280\) |
2.3.0.a.1, 8.6.0.d.1, 339762.6.0.?, 1359048.12.0.? |
$[(341993/88, 26519511/88)]$ |
$1$ |
| 339762.a2 |
339762a2 |
339762.a |
339762a |
$2$ |
$2$ |
\( 2 \cdot 3 \cdot 17 \cdot 3331 \) |
\( - 2^{11} \cdot 3^{2} \cdot 17^{2} \cdot 3331^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.5 |
2B |
$1359048$ |
$12$ |
$0$ |
$6.472318015$ |
$1$ |
|
$0$ |
$1071488$ |
$1.328352$ |
$44515050822657143/59104366921728$ |
$0.87401$ |
$3.03020$ |
$1$ |
$[1, 1, 0, 7384, 280896]$ |
\(y^2+xy=x^3+x^2+7384x+280896\) |
2.3.0.a.1, 8.6.0.a.1, 679524.6.0.?, 1359048.12.0.? |
$[(1525/4, 84279/4)]$ |
$1$ |
| 339762.b1 |
339762b1 |
339762.b |
339762b |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 17 \cdot 3331 \) |
\( - 2^{2} \cdot 3^{2} \cdot 17^{2} \cdot 3331 \) |
$3$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$6662$ |
$2$ |
$0$ |
$0.976927783$ |
$1$ |
|
$30$ |
$136704$ |
$0.126313$ |
$494913671/34655724$ |
$0.78005$ |
$1.94782$ |
$1$ |
$[1, 1, 0, 17, 289]$ |
\(y^2+xy=x^3+x^2+17x+289\) |
6662.2.0.? |
$[(0, 17), (34, 187), (4, 19)]$ |
$1$ |
| 339762.c1 |
339762c1 |
339762.c |
339762c |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 17 \cdot 3331 \) |
\( 2 \cdot 3^{10} \cdot 17 \cdot 3331 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$453016$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$430400$ |
$0.677381$ |
$339615493483609/6687535446$ |
$0.82409$ |
$2.62711$ |
$1$ |
$[1, 1, 0, -1453, -21569]$ |
\(y^2+xy=x^3+x^2-1453x-21569\) |
453016.2.0.? |
$[ ]$ |
$1$ |
| 339762.d1 |
339762d1 |
339762.d |
339762d |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 17 \cdot 3331 \) |
\( 2^{9} \cdot 3^{4} \cdot 17 \cdot 3331 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$453016$ |
$2$ |
$0$ |
$2.759526238$ |
$1$ |
|
$2$ |
$259200$ |
$0.569921$ |
$68523370149961/2348434944$ |
$0.88774$ |
$2.50143$ |
$1$ |
$[1, 1, 0, -852, -9648]$ |
\(y^2+xy=x^3+x^2-852x-9648\) |
453016.2.0.? |
$[(-19, 21)]$ |
$1$ |
| 339762.e1 |
339762e1 |
339762.e |
339762e |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 17 \cdot 3331 \) |
\( 2^{31} \cdot 3^{2} \cdot 17 \cdot 3331 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$453016$ |
$2$ |
$0$ |
$6.701413933$ |
$1$ |
|
$2$ |
$2172480$ |
$1.575472$ |
$1912428169368401593/1094450008817664$ |
$0.92385$ |
$3.30519$ |
$1$ |
$[1, 0, 1, -25860, -170750]$ |
\(y^2+xy+y=x^3-25860x-170750\) |
453016.2.0.? |
$[(1334, 47703)]$ |
$1$ |
| 339762.f1 |
339762f1 |
339762.f |
339762f |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 17 \cdot 3331 \) |
\( 2 \cdot 3^{6} \cdot 17^{7} \cdot 3331 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$453016$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$2366784$ |
$1.685219$ |
$30192983848718376841/1992849978614454$ |
$0.89612$ |
$3.52184$ |
$1$ |
$[1, 0, 1, -64873, -5991490]$ |
\(y^2+xy+y=x^3-64873x-5991490\) |
453016.2.0.? |
$[ ]$ |
$1$ |
| 339762.g1 |
339762g1 |
339762.g |
339762g |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 17 \cdot 3331 \) |
\( - 2^{4} \cdot 3^{4} \cdot 17^{2} \cdot 3331 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$6662$ |
$2$ |
$0$ |
$0.431187233$ |
$1$ |
|
$6$ |
$353280$ |
$0.432811$ |
$1407563886743/1247606064$ |
$0.79481$ |
$2.19636$ |
$1$ |
$[1, 0, 1, 233, -982]$ |
\(y^2+xy+y=x^3+233x-982\) |
6662.2.0.? |
$[(19, 92)]$ |
$1$ |
| 339762.h1 |
339762h1 |
339762.h |
339762h |
$2$ |
$2$ |
\( 2 \cdot 3 \cdot 17 \cdot 3331 \) |
\( 2^{18} \cdot 3^{3} \cdot 17^{2} \cdot 3331 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.4 |
2B |
$79944$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$5287680$ |
$1.811365$ |
$17542763799911540830801/6813592584192$ |
$0.92422$ |
$4.02159$ |
$1$ |
$[1, 1, 1, -541325, -153523069]$ |
\(y^2+xy+y=x^3+x^2-541325x-153523069\) |
2.3.0.a.1, 8.6.0.d.1, 19986.6.0.?, 79944.12.0.? |
$[ ]$ |
$1$ |
| 339762.h2 |
339762h2 |
339762.h |
339762h |
$2$ |
$2$ |
\( 2 \cdot 3 \cdot 17 \cdot 3331 \) |
\( - 2^{9} \cdot 3^{6} \cdot 17^{4} \cdot 3331^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.5 |
2B |
$79944$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$10575360$ |
$2.157940$ |
$-17295052580084439585361/345893531317682688$ |
$0.92449$ |
$4.02314$ |
$1$ |
$[1, 1, 1, -538765, -155043709]$ |
\(y^2+xy+y=x^3+x^2-538765x-155043709\) |
2.3.0.a.1, 8.6.0.a.1, 39972.6.0.?, 79944.12.0.? |
$[ ]$ |
$1$ |
| 339762.i1 |
339762i1 |
339762.i |
339762i |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 17 \cdot 3331 \) |
\( 2^{9} \cdot 3^{6} \cdot 17^{3} \cdot 3331 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$453016$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$15116544$ |
$2.498833$ |
$757179020241422017727154913/6108279289344$ |
$0.96236$ |
$4.85958$ |
$1$ |
$[1, 1, 1, -18988542, -31856159685]$ |
\(y^2+xy+y=x^3+x^2-18988542x-31856159685\) |
453016.2.0.? |
$[ ]$ |
$1$ |
| 339762.j1 |
339762j1 |
339762.j |
339762j |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 17 \cdot 3331 \) |
\( 2^{3} \cdot 3^{24} \cdot 17^{5} \cdot 3331 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$453016$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$230480640$ |
$4.094414$ |
$93975577734076957845877490195798449/10686102605099672126616$ |
$1.00858$ |
$6.32289$ |
$1$ |
$[1, 1, 1, -9471754451, 354804344400377]$ |
\(y^2+xy+y=x^3+x^2-9471754451x+354804344400377\) |
453016.2.0.? |
$[ ]$ |
$1$ |
| 339762.k1 |
339762k1 |
339762.k |
339762k |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 17 \cdot 3331 \) |
\( 2^{5} \cdot 3^{2} \cdot 17^{3} \cdot 3331 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$453016$ |
$2$ |
$0$ |
$1.893110452$ |
$1$ |
|
$4$ |
$360000$ |
$0.693437$ |
$746661031875361/4713178464$ |
$0.82983$ |
$2.68896$ |
$1$ |
$[1, 1, 1, -1890, -32241]$ |
\(y^2+xy+y=x^3+x^2-1890x-32241\) |
453016.2.0.? |
$[(-27, 15)]$ |
$1$ |
| 339762.l1 |
339762l1 |
339762.l |
339762l |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 17 \cdot 3331 \) |
\( 2 \cdot 3^{2} \cdot 17 \cdot 3331 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$453016$ |
$2$ |
$0$ |
$2.674574473$ |
$1$ |
|
$0$ |
$38528$ |
$-0.155344$ |
$1948441249/1019286$ |
$0.72782$ |
$1.67951$ |
$1$ |
$[1, 0, 0, -26, -18]$ |
\(y^2+xy=x^3-26x-18\) |
453016.2.0.? |
$[(-17/2, 53/2)]$ |
$1$ |
| 339762.m1 |
339762m2 |
339762.m |
339762m |
$2$ |
$7$ |
\( 2 \cdot 3 \cdot 17 \cdot 3331 \) |
\( 2 \cdot 3^{2} \cdot 17 \cdot 3331^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$7$ |
7.48.0.5 |
7B.1.3 |
$3171112$ |
$96$ |
$2$ |
$1$ |
$196$ |
$2, 7$ |
$0$ |
$306252352$ |
$4.169670$ |
$3314059238965717412166686272528609/1392335368399818889959574566$ |
$1.00166$ |
$6.06026$ |
$1$ |
$[1, 0, 0, -3106076766, -66605543437698]$ |
\(y^2+xy=x^3-3106076766x-66605543437698\) |
7.48.0-7.a.2.2, 453016.2.0.?, 3171112.96.2.? |
$[ ]$ |
$1$ |
| 339762.m2 |
339762m1 |
339762.m |
339762m |
$2$ |
$7$ |
\( 2 \cdot 3 \cdot 17 \cdot 3331 \) |
\( 2^{7} \cdot 3^{14} \cdot 17^{7} \cdot 3331 \) |
$0$ |
$\Z/7\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$7$ |
7.48.0.1 |
7B.1.1 |
$3171112$ |
$96$ |
$2$ |
$1$ |
$4$ |
$2$ |
$6$ |
$43750336$ |
$3.196712$ |
$124976563139916356014105311169/836805677420123692416$ |
$0.97711$ |
$5.26052$ |
$1$ |
$[1, 0, 0, -104160156, 409155902352]$ |
\(y^2+xy=x^3-104160156x+409155902352\) |
7.48.0-7.a.1.2, 453016.2.0.?, 3171112.96.2.? |
$[ ]$ |
$1$ |
| 339762.n1 |
339762n2 |
339762.n |
339762n |
$2$ |
$5$ |
\( 2 \cdot 3 \cdot 17 \cdot 3331 \) |
\( - 2 \cdot 3^{2} \cdot 17 \cdot 3331^{5} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$5$ |
5.24.0.3 |
5B.1.2 |
$2265080$ |
$48$ |
$1$ |
$25.66062668$ |
$1$ |
|
$0$ |
$10980000$ |
$2.551498$ |
$-116833789079008796976481/125485801790447449206$ |
$0.94161$ |
$4.25286$ |
$1$ |
$[1, 0, 0, -1018470, -668654982]$ |
\(y^2+xy=x^3-1018470x-668654982\) |
5.24.0-5.a.2.2, 453016.2.0.?, 2265080.48.1.? |
$[(138085866539/1430, 51208156284952753/1430)]$ |
$1$ |
| 339762.n2 |
339762n1 |
339762.n |
339762n |
$2$ |
$5$ |
\( 2 \cdot 3 \cdot 17 \cdot 3331 \) |
\( - 2^{5} \cdot 3^{10} \cdot 17^{5} \cdot 3331 \) |
$1$ |
$\Z/5\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$5$ |
5.24.0.1 |
5B.1.1 |
$2265080$ |
$48$ |
$1$ |
$5.132125336$ |
$1$ |
|
$8$ |
$2196000$ |
$1.746780$ |
$-2576316837405507841/8936794367765856$ |
$0.98693$ |
$3.48131$ |
$1$ |
$[1, 0, 0, -28560, 4910688]$ |
\(y^2+xy=x^3-28560x+4910688\) |
5.24.0-5.a.1.2, 453016.2.0.?, 2265080.48.1.? |
$[(-82, 2630)]$ |
$1$ |
| 339762.o1 |
339762o2 |
339762.o |
339762o |
$2$ |
$3$ |
\( 2 \cdot 3 \cdot 17 \cdot 3331 \) |
\( 2^{3} \cdot 3^{4} \cdot 17 \cdot 3331^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
3.8.0.2 |
3B.1.2 |
$1359048$ |
$16$ |
$0$ |
$5.591316735$ |
$1$ |
|
$0$ |
$9704448$ |
$2.256687$ |
$5790755826307787165559217/407143799620056$ |
$0.94634$ |
$4.47694$ |
$1$ |
$[1, 0, 0, -3741139, -2785495543]$ |
\(y^2+xy=x^3-3741139x-2785495543\) |
3.8.0-3.a.1.1, 453016.2.0.?, 1359048.16.0.? |
$[(-27916/5, 70963/5)]$ |
$1$ |
| 339762.o2 |
339762o1 |
339762.o |
339762o |
$2$ |
$3$ |
\( 2 \cdot 3 \cdot 17 \cdot 3331 \) |
\( 2^{9} \cdot 3^{12} \cdot 17^{3} \cdot 3331 \) |
$1$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
3.8.0.1 |
3B.1.1 |
$1359048$ |
$16$ |
$0$ |
$1.863772245$ |
$1$ |
|
$6$ |
$3234816$ |
$1.707380$ |
$14480270626688337457/4452935601931776$ |
$0.89814$ |
$3.46414$ |
$1$ |
$[1, 0, 0, -50779, -3019183]$ |
\(y^2+xy=x^3-50779x-3019183\) |
3.8.0-3.a.1.2, 453016.2.0.?, 1359048.16.0.? |
$[(-166, 1001)]$ |
$1$ |
| 339762.p1 |
339762p1 |
339762.p |
339762p |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 17 \cdot 3331 \) |
\( 2^{7} \cdot 3^{12} \cdot 17 \cdot 3331 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$453016$ |
$2$ |
$0$ |
$0.446546926$ |
$1$ |
|
$4$ |
$887040$ |
$1.104437$ |
$6656660819158897/3852020416896$ |
$0.95382$ |
$2.86074$ |
$1$ |
$[1, 0, 0, -3919, 377]$ |
\(y^2+xy=x^3-3919x+377\) |
453016.2.0.? |
$[(-16, 251)]$ |
$1$ |
