| 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 |
| 33135.a1 |
33135d1 |
33135.a |
33135d |
$1$ |
$1$ |
\( 3 \cdot 5 \cdot 47^{2} \) |
\( - 3^{8} \cdot 5 \cdot 47^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$470$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1371648$ |
$2.560017$ |
$-2342039552/32805$ |
$1.19328$ |
$5.40427$ |
$[0, -1, 1, -2872436, 1897300916]$ |
\(y^2+y=x^3-x^2-2872436x+1897300916\) |
470.2.0.? |
$[]$ |
| 33135.b1 |
33135g1 |
33135.b |
33135g |
$1$ |
$1$ |
\( 3 \cdot 5 \cdot 47^{2} \) |
\( - 3^{8} \cdot 5 \cdot 47^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$470$ |
$2$ |
$0$ |
$1.056855539$ |
$1$ |
|
$4$ |
$29184$ |
$0.634945$ |
$-2342039552/32805$ |
$1.19328$ |
$3.18481$ |
$[0, -1, 1, -1300, -17832]$ |
\(y^2+y=x^3-x^2-1300x-17832\) |
470.2.0.? |
$[(157, 1903)]$ |
| 33135.c1 |
33135c1 |
33135.c |
33135c |
$1$ |
$1$ |
\( 3 \cdot 5 \cdot 47^{2} \) |
\( - 3^{3} \cdot 5^{3} \cdot 47^{11} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$2820$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$3179520$ |
$2.885250$ |
$-191202526081/774039398625$ |
$1.04515$ |
$5.56579$ |
$[1, 1, 1, -265126, -4395165052]$ |
\(y^2+xy+y=x^3+x^2-265126x-4395165052\) |
2820.2.0.? |
$[]$ |
| 33135.d1 |
33135a8 |
33135.d |
33135a |
$8$ |
$16$ |
\( 3 \cdot 5 \cdot 47^{2} \) |
\( 3^{4} \cdot 5 \cdot 47^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.48.0.121 |
2B |
$22560$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$0$ |
$412160$ |
$2.215942$ |
$1114544804970241/405$ |
$1.07354$ |
$5.54825$ |
$[1, 1, 1, -4771486, 4009713254]$ |
\(y^2+xy+y=x^3+x^2-4771486x+4009713254\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 10.6.0.a.1, 16.48.0.x.2, $\ldots$ |
$[]$ |
| 33135.d2 |
33135a6 |
33135.d |
33135a |
$8$ |
$16$ |
\( 3 \cdot 5 \cdot 47^{2} \) |
\( 3^{8} \cdot 5^{2} \cdot 47^{6} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.48.0.123 |
2Cs |
$11280$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$2$ |
$206080$ |
$1.869370$ |
$272223782641/164025$ |
$1.03897$ |
$4.74915$ |
$[1, 1, 1, -298261, 62539514]$ |
\(y^2+xy+y=x^3+x^2-298261x+62539514\) |
2.6.0.a.1, 4.12.0.b.1, 8.48.0.k.1, 20.24.0.c.1, 40.96.1.cc.2, $\ldots$ |
$[]$ |
| 33135.d3 |
33135a7 |
33135.d |
33135a |
$8$ |
$16$ |
\( 3 \cdot 5 \cdot 47^{2} \) |
\( - 3^{16} \cdot 5 \cdot 47^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.48.0.134 |
2B |
$22560$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$0$ |
$412160$ |
$2.215942$ |
$-147281603041/215233605$ |
$1.05949$ |
$4.81118$ |
$[1, 1, 1, -243036, 86485074]$ |
\(y^2+xy+y=x^3+x^2-243036x+86485074\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0.ba.2, 16.48.0.u.2, 20.12.0.h.1, $\ldots$ |
$[]$ |
| 33135.d4 |
33135a4 |
33135.d |
33135a |
$8$ |
$16$ |
\( 3 \cdot 5 \cdot 47^{2} \) |
\( 3 \cdot 5 \cdot 47^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
32.48.0.1 |
2B |
$22560$ |
$768$ |
$13$ |
$1$ |
$4$ |
$2$ |
$0$ |
$103040$ |
$1.522797$ |
$56667352321/15$ |
$1.03019$ |
$4.59836$ |
$[1, 1, 1, -176766, -28678932]$ |
\(y^2+xy+y=x^3+x^2-176766x-28678932\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.g.1, 24.24.0.by.2, $\ldots$ |
$[]$ |
| 33135.d5 |
33135a3 |
33135.d |
33135a |
$8$ |
$16$ |
\( 3 \cdot 5 \cdot 47^{2} \) |
\( 3^{4} \cdot 5^{4} \cdot 47^{6} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.48.0.44 |
2Cs |
$11280$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$2$ |
$103040$ |
$1.522797$ |
$111284641/50625$ |
$1.02534$ |
$3.99953$ |
$[1, 1, 1, -22136, 577064]$ |
\(y^2+xy+y=x^3+x^2-22136x+577064\) |
2.6.0.a.1, 4.24.0.b.1, 8.48.0.b.2, 24.96.1.n.1, 40.96.1.s.1, $\ldots$ |
$[]$ |
| 33135.d6 |
33135a2 |
33135.d |
33135a |
$8$ |
$16$ |
\( 3 \cdot 5 \cdot 47^{2} \) |
\( 3^{2} \cdot 5^{2} \cdot 47^{6} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.48.0.3 |
2Cs |
$11280$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$2$ |
$51520$ |
$1.176222$ |
$13997521/225$ |
$0.96230$ |
$3.80034$ |
$[1, 1, 1, -11091, -447912]$ |
\(y^2+xy+y=x^3+x^2-11091x-447912\) |
2.6.0.a.1, 4.12.0.b.1, 8.24.0.i.1, 16.48.0.d.2, 24.48.0.bb.2, $\ldots$ |
$[]$ |
| 33135.d7 |
33135a1 |
33135.d |
33135a |
$8$ |
$16$ |
\( 3 \cdot 5 \cdot 47^{2} \) |
\( - 3 \cdot 5 \cdot 47^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
32.48.0.1 |
2B |
$22560$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$1$ |
$25760$ |
$0.829649$ |
$-1/15$ |
$1.19808$ |
$3.19587$ |
$[1, 1, 1, -46, -19366]$ |
\(y^2+xy+y=x^3+x^2-46x-19366\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.g.1, 24.24.0.bz.1, $\ldots$ |
$[]$ |
| 33135.d8 |
33135a5 |
33135.d |
33135a |
$8$ |
$16$ |
\( 3 \cdot 5 \cdot 47^{2} \) |
\( - 3^{2} \cdot 5^{8} \cdot 47^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.48.0.197 |
2B |
$22560$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$0$ |
$206080$ |
$1.869370$ |
$4733169839/3515625$ |
$1.05585$ |
$4.35984$ |
$[1, 1, 1, 77269, 4433978]$ |
\(y^2+xy+y=x^3+x^2+77269x+4433978\) |
2.3.0.a.1, 4.12.0.d.1, 8.48.0.n.2, 24.96.1.cv.2, 80.96.1.?, $\ldots$ |
$[]$ |
| 33135.e1 |
33135b1 |
33135.e |
33135b |
$1$ |
$1$ |
\( 3 \cdot 5 \cdot 47^{2} \) |
\( 3^{6} \cdot 5^{3} \cdot 47^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$10$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$27648$ |
$0.766729$ |
$11679607249441/91125$ |
$0.96930$ |
$3.63066$ |
$[1, 1, 1, -6156, -188472]$ |
\(y^2+xy+y=x^3+x^2-6156x-188472\) |
10.2.0.a.1 |
$[]$ |
| 33135.f1 |
33135f1 |
33135.f |
33135f |
$1$ |
$1$ |
\( 3 \cdot 5 \cdot 47^{2} \) |
\( 3^{6} \cdot 5^{3} \cdot 47^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$10$ |
$2$ |
$0$ |
$2.785490667$ |
$1$ |
|
$2$ |
$1299456$ |
$2.691803$ |
$11679607249441/91125$ |
$0.96930$ |
$5.85012$ |
$[1, 1, 1, -13598650, 19295737010]$ |
\(y^2+xy+y=x^3+x^2-13598650x+19295737010\) |
10.2.0.a.1 |
$[(2123, -792)]$ |
| 33135.g1 |
33135m1 |
33135.g |
33135m |
$1$ |
$1$ |
\( 3 \cdot 5 \cdot 47^{2} \) |
\( - 3^{5} \cdot 5 \cdot 47^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$2820$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$176640$ |
$1.652874$ |
$-5168743489/57105$ |
$0.86431$ |
$4.37012$ |
$[1, 0, 0, -79570, -8727883]$ |
\(y^2+xy=x^3-79570x-8727883\) |
2820.2.0.? |
$[]$ |
| 33135.h1 |
33135e1 |
33135.h |
33135e |
$1$ |
$1$ |
\( 3 \cdot 5 \cdot 47^{2} \) |
\( - 3^{14} \cdot 5^{5} \cdot 47^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$470$ |
$2$ |
$0$ |
$5.656027591$ |
$1$ |
|
$0$ |
$1854720$ |
$2.973125$ |
$-21370158463320064/702498571875$ |
$1.13158$ |
$5.83733$ |
$[0, -1, 1, -12770965, -18054214782]$ |
\(y^2+y=x^3-x^2-12770965x-18054214782\) |
470.2.0.? |
$[(1927636/13, 2524239769/13)]$ |
| 33135.i1 |
33135j2 |
33135.i |
33135j |
$2$ |
$3$ |
\( 3 \cdot 5 \cdot 47^{2} \) |
\( - 3^{2} \cdot 5^{3} \cdot 47^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$1410$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$582912$ |
$2.162613$ |
$-59501707264/116800875$ |
$0.98675$ |
$4.74523$ |
$[0, 1, 1, -179665, 61369681]$ |
\(y^2+y=x^3+x^2-179665x+61369681\) |
3.4.0.a.1, 30.8.0-3.a.1.2, 141.8.0.?, 470.2.0.?, 1410.16.0.? |
$[]$ |
| 33135.i2 |
33135j1 |
33135.i |
33135j |
$2$ |
$3$ |
\( 3 \cdot 5 \cdot 47^{2} \) |
\( - 3^{6} \cdot 5 \cdot 47^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$1410$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$194304$ |
$1.613304$ |
$71991296/171315$ |
$0.88453$ |
$4.06676$ |
$[0, 1, 1, 19145, -1792256]$ |
\(y^2+y=x^3+x^2+19145x-1792256\) |
3.4.0.a.1, 30.8.0-3.a.1.1, 141.8.0.?, 470.2.0.?, 1410.16.0.? |
$[]$ |
| 33135.j1 |
33135h4 |
33135.j |
33135h |
$4$ |
$4$ |
\( 3 \cdot 5 \cdot 47^{2} \) |
\( 3 \cdot 5^{12} \cdot 47^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$5640$ |
$48$ |
$0$ |
$21.18983551$ |
$1$ |
|
$0$ |
$953856$ |
$2.657116$ |
$138356873478361/34423828125$ |
$0.95474$ |
$5.34780$ |
$[1, 0, 1, -2380244, 1066993817]$ |
\(y^2+xy+y=x^3-2380244x+1066993817\) |
2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 40.12.0.ba.1, 120.24.0.?, $\ldots$ |
$[(-21663965087/10656, 47198585905786817/10656)]$ |
| 33135.j2 |
33135h2 |
33135.j |
33135h |
$4$ |
$4$ |
\( 3 \cdot 5 \cdot 47^{2} \) |
\( 3^{2} \cdot 5^{6} \cdot 47^{8} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.6.0.1 |
2Cs |
$2820$ |
$48$ |
$0$ |
$42.37967102$ |
$1$ |
|
$2$ |
$476928$ |
$2.310539$ |
$5717095008841/310640625$ |
$0.92720$ |
$5.04166$ |
$[1, 0, 1, -822899, -273568759]$ |
\(y^2+xy+y=x^3-822899x-273568759\) |
2.6.0.a.1, 12.12.0-2.a.1.1, 20.12.0.a.1, 60.24.0-20.a.1.3, 188.12.0.?, $\ldots$ |
$[(-54222070677332478777/297038974, 17960867701249327495770966187/297038974)]$ |
| 33135.j3 |
33135h1 |
33135.j |
33135h |
$4$ |
$4$ |
\( 3 \cdot 5 \cdot 47^{2} \) |
\( 3 \cdot 5^{3} \cdot 47^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$5640$ |
$48$ |
$0$ |
$84.75934205$ |
$1$ |
|
$1$ |
$238464$ |
$1.963966$ |
$5489965305721/17625$ |
$0.92547$ |
$5.03777$ |
$[1, 0, 1, -811854, -281622773]$ |
\(y^2+xy+y=x^3-811854x-281622773\) |
2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 40.12.0.ba.1, 120.24.0.?, $\ldots$ |
$[(302882775884717209961406519232399051015/42379481431388057, 5264739244530019393504282875583564583223989237063481960868/42379481431388057)]$ |
| 33135.j4 |
33135h3 |
33135.j |
33135h |
$4$ |
$4$ |
\( 3 \cdot 5 \cdot 47^{2} \) |
\( - 3^{4} \cdot 5^{3} \cdot 47^{10} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$5640$ |
$48$ |
$0$ |
$21.18983551$ |
$1$ |
|
$0$ |
$953856$ |
$2.657116$ |
$1779919481159/49406770125$ |
$0.98151$ |
$5.29939$ |
$[1, 0, 1, 557726, -1098630259]$ |
\(y^2+xy+y=x^3+557726x-1098630259\) |
2.3.0.a.1, 4.6.0.c.1, 20.12.0.h.1, 24.12.0-4.c.1.3, 120.24.0.?, $\ldots$ |
$[(131389146589/7457, 47531895738074476/7457)]$ |
| 33135.k1 |
33135i1 |
33135.k |
33135i |
$1$ |
$1$ |
\( 3 \cdot 5 \cdot 47^{2} \) |
\( 3^{14} \cdot 5^{3} \cdot 47^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$10$ |
$2$ |
$0$ |
$0.725140763$ |
$1$ |
|
$2$ |
$96768$ |
$1.387154$ |
$9993948576518041/597871125$ |
$1.00470$ |
$4.27936$ |
$[1, 0, 1, -58444, 5433017]$ |
\(y^2+xy+y=x^3-58444x+5433017\) |
10.2.0.a.1 |
$[(115, 428)]$ |
| 33135.l1 |
33135l1 |
33135.l |
33135l |
$1$ |
$1$ |
\( 3 \cdot 5 \cdot 47^{2} \) |
\( - 3 \cdot 5^{3} \cdot 47^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$2820$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$105984$ |
$1.429234$ |
$30080231/17625$ |
$0.88780$ |
$3.87384$ |
$[1, 0, 1, 14312, -72469]$ |
\(y^2+xy+y=x^3+14312x-72469\) |
2820.2.0.? |
$[]$ |
| 33135.m1 |
33135k1 |
33135.m |
33135k |
$1$ |
$1$ |
\( 3 \cdot 5 \cdot 47^{2} \) |
\( 3^{14} \cdot 5^{3} \cdot 47^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$10$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$4548096$ |
$3.312225$ |
$9993948576518041/597871125$ |
$1.00470$ |
$6.49882$ |
$[1, 0, 1, -129101738, -564588556837]$ |
\(y^2+xy+y=x^3-129101738x-564588556837\) |
10.2.0.a.1 |
$[]$ |
