LMFDB - Elliptic curve search results

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Conductor	Discriminant	j-invariant	Rank

Bad$\ p$	Curves per isogeny class	Complex multiplication	Torsion

Isogeny class degree	Cyclic isogeny degree	Isogeny class size	Integral points

Analytic order of Ш	$p\ $div$\ $\|Ш\|	Regulator	Reduction	Faltings height

Galois image	Adelic level	Adelic index	Adelic genus

Nonmax$\ \ell$	$abc$ quality	Szpiro ratio

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Results (36 matches)

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	Sato-Tate	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
1824.b1	1824g1	1824.b	1824g	$1$	$1$	$ 2^{5} \cdot 3 \cdot 19 $	$ - 2^{12} \cdot 3^{4} \cdot 19 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$38$	$2$	$0$	$0.509373222$	$1$	$4$	$256$	$-0.013975$	$175616/1539$	$0.88880$	$3.06881$	$[0, -1, 0, 19, -123]$	$y^2=x^3-x^2+19x-123$	38.2.0.a.1	$[(11, 36)]$
1824.i1	1824h1	1824.i	1824h	$1$	$1$	$ 2^{5} \cdot 3 \cdot 19 $	$ - 2^{12} \cdot 3^{4} \cdot 19 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$38$	$2$	$0$	$0.233487045$	$1$	$6$	$256$	$-0.013975$	$175616/1539$	$0.88880$	$3.06881$	$[0, 1, 0, 19, 123]$	$y^2=x^3+x^2+19x+123$	38.2.0.a.1	$[(1, 12)]$
3648.m1	3648z1	3648.m	3648z	$1$	$1$	$ 2^{6} \cdot 3 \cdot 19 $	$ - 2^{6} \cdot 3^{4} \cdot 19 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$38$	$2$	$0$	$0.680980560$	$1$	$2$	$256$	$-0.360548$	$175616/1539$	$0.88880$	$2.30240$	$[0, -1, 0, 5, 13]$	$y^2=x^3-x^2+5x+13$	38.2.0.a.1	$[(4, 9)]$
3648.bd1	3648bd1	3648.bd	3648bd	$1$	$1$	$ 2^{6} \cdot 3 \cdot 19 $	$ - 2^{6} \cdot 3^{4} \cdot 19 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$38$	$2$	$0$	$0.627823039$	$1$	$2$	$256$	$-0.360548$	$175616/1539$	$0.88880$	$2.30240$	$[0, 1, 0, 5, -13]$	$y^2=x^3+x^2+5x-13$	38.2.0.a.1	$[(2, 3)]$
5472.n1	5472k1	5472.n	5472k	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 19 $	$ - 2^{12} \cdot 3^{10} \cdot 19 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$38$	$2$	$0$	$0.991152930$	$1$	$4$	$2048$	$0.535331$	$175616/1539$	$0.88880$	$3.44294$	$[0, 0, 0, 168, 3152]$	$y^2=x^3+168x+3152$	38.2.0.a.1	$[(-8, 36)]$
5472.r1	5472d1	5472.r	5472d	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 19 $	$ - 2^{12} \cdot 3^{10} \cdot 19 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$38$	$2$	$0$	$1$	$1$	$0$	$2048$	$0.535331$	$175616/1539$	$0.88880$	$3.44294$	$[0, 0, 0, 168, -3152]$	$y^2=x^3+168x-3152$	38.2.0.a.1	$[]$
10944.v1	10944bu1	10944.v	10944bu	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 19 $	$ - 2^{6} \cdot 3^{10} \cdot 19 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$38$	$2$	$0$	$1.505943884$	$1$	$2$	$2048$	$0.188757$	$175616/1539$	$0.88880$	$2.73918$	$[0, 0, 0, 42, 394]$	$y^2=x^3+42x+394$	38.2.0.a.1	$[(5, 27)]$
10944.x1	10944cl1	10944.x	10944cl	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 19 $	$ - 2^{6} \cdot 3^{10} \cdot 19 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$38$	$2$	$0$	$1$	$1$	$0$	$2048$	$0.188757$	$175616/1539$	$0.88880$	$2.73918$	$[0, 0, 0, 42, -394]$	$y^2=x^3+42x-394$	38.2.0.a.1	$[]$
34656.c1	34656f1	34656.c	34656f	$1$	$1$	$ 2^{5} \cdot 3 \cdot 19^{2} $	$ - 2^{12} \cdot 3^{4} \cdot 19^{7} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$38$	$2$	$0$	$1.666971224$	$1$	$12$	$92160$	$1.458244$	$175616/1539$	$0.88880$	$3.89446$	$[0, -1, 0, 6739, -802971]$	$y^2=x^3-x^2+6739x-802971$	38.2.0.a.1	$[(127, 1444), (95, 828)]$
34656.s1	34656o1	34656.s	34656o	$1$	$1$	$ 2^{5} \cdot 3 \cdot 19^{2} $	$ - 2^{12} \cdot 3^{4} \cdot 19^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$38$	$2$	$0$	$0.984226145$	$1$	$4$	$92160$	$1.458244$	$175616/1539$	$0.88880$	$3.89446$	$[0, 1, 0, 6739, 802971]$	$y^2=x^3+x^2+6739x+802971$	38.2.0.a.1	$[(253, 4332)]$
45600.k1	45600a1	45600.k	45600a	$1$	$1$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 19 $	$ - 2^{12} \cdot 3^{4} \cdot 5^{6} \cdot 19 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$38$	$2$	$0$	$1.505425367$	$1$	$4$	$35840$	$0.790744$	$175616/1539$	$0.88880$	$3.04816$	$[0, -1, 0, 467, 14437]$	$y^2=x^3-x^2+467x+14437$	38.2.0.a.1	$[(-17, 36)]$
45600.bn1	45600r1	45600.bn	45600r	$1$	$1$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 19 $	$ - 2^{12} \cdot 3^{4} \cdot 5^{6} \cdot 19 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$38$	$2$	$0$	$2.009350965$	$1$	$2$	$35840$	$0.790744$	$175616/1539$	$0.88880$	$3.04816$	$[0, 1, 0, 467, -14437]$	$y^2=x^3+x^2+467x-14437$	38.2.0.a.1	$[(29, 156)]$
69312.bi1	69312cn1	69312.bi	69312cn	$1$	$1$	$ 2^{6} \cdot 3 \cdot 19^{2} $	$ - 2^{6} \cdot 3^{4} \cdot 19^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$38$	$2$	$0$	$1.028175163$	$1$	$0$	$92160$	$1.111671$	$175616/1539$	$0.88880$	$3.27917$	$[0, -1, 0, 1685, 99529]$	$y^2=x^3-x^2+1685x+99529$	38.2.0.a.1	$[(109/2, 3249/2)]$
69312.dj1	69312dj1	69312.dj	69312dj	$1$	$1$	$ 2^{6} \cdot 3 \cdot 19^{2} $	$ - 2^{6} \cdot 3^{4} \cdot 19^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$38$	$2$	$0$	$1$	$1$	$0$	$92160$	$1.111671$	$175616/1539$	$0.88880$	$3.27917$	$[0, 1, 0, 1685, -99529]$	$y^2=x^3+x^2+1685x-99529$	38.2.0.a.1	$[]$
89376.z1	89376bu1	89376.z	89376bu	$1$	$1$	$ 2^{5} \cdot 3 \cdot 7^{2} \cdot 19 $	$ - 2^{12} \cdot 3^{4} \cdot 7^{6} \cdot 19 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$38$	$2$	$0$	$1$	$1$	$0$	$96768$	$0.958980$	$175616/1539$	$0.88880$	$3.04532$	$[0, -1, 0, 915, -40347]$	$y^2=x^3-x^2+915x-40347$	38.2.0.a.1	$[]$
89376.co1	89376ck1	89376.co	89376ck	$1$	$1$	$ 2^{5} \cdot 3 \cdot 7^{2} \cdot 19 $	$ - 2^{12} \cdot 3^{4} \cdot 7^{6} \cdot 19 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$38$	$2$	$0$	$1$	$1$	$0$	$96768$	$0.958980$	$175616/1539$	$0.88880$	$3.04532$	$[0, 1, 0, 915, 40347]$	$y^2=x^3+x^2+915x+40347$	38.2.0.a.1	$[]$
91200.da1	91200fc1	91200.da	91200fc	$1$	$1$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 19 $	$ - 2^{6} \cdot 3^{4} \cdot 5^{6} \cdot 19 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$38$	$2$	$0$	$1$	$1$	$0$	$35840$	$0.444170$	$175616/1539$	$0.88880$	$2.49902$	$[0, -1, 0, 117, -1863]$	$y^2=x^3-x^2+117x-1863$	38.2.0.a.1	$[]$
91200.gl1	91200ib1	91200.gl	91200ib	$1$	$1$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 19 $	$ - 2^{6} \cdot 3^{4} \cdot 5^{6} \cdot 19 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$38$	$2$	$0$	$1$	$1$	$0$	$35840$	$0.444170$	$175616/1539$	$0.88880$	$2.49902$	$[0, 1, 0, 117, 1863]$	$y^2=x^3+x^2+117x+1863$	38.2.0.a.1	$[]$
103968.bt1	103968bx1	103968.bt	103968bx	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 19^{2} $	$ - 2^{12} \cdot 3^{10} \cdot 19^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$38$	$2$	$0$	$1$	$1$	$0$	$737280$	$2.007549$	$175616/1539$	$0.88880$	$4.09470$	$[0, 0, 0, 60648, -21619568]$	$y^2=x^3+60648x-21619568$	38.2.0.a.1	$[]$
103968.bx1	103968bv1	103968.bx	103968bv	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 19^{2} $	$ - 2^{12} \cdot 3^{10} \cdot 19^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$38$	$2$	$0$	$1$	$1$	$0$	$737280$	$2.007549$	$175616/1539$	$0.88880$	$4.09470$	$[0, 0, 0, 60648, 21619568]$	$y^2=x^3+60648x+21619568$	38.2.0.a.1	$[]$
136800.bi1	136800v1	136800.bi	136800v	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 19 $	$ - 2^{12} \cdot 3^{10} \cdot 5^{6} \cdot 19 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$38$	$2$	$0$	$4.890667470$	$1$	$2$	$286720$	$1.340050$	$175616/1539$	$0.88880$	$3.32238$	$[0, 0, 0, 4200, -394000]$	$y^2=x^3+4200x-394000$	38.2.0.a.1	$[(1084, 35748)]$
136800.ca1	136800z1	136800.ca	136800z	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 19 $	$ - 2^{12} \cdot 3^{10} \cdot 5^{6} \cdot 19 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$38$	$2$	$0$	$1$	$1$	$0$	$286720$	$1.340050$	$175616/1539$	$0.88880$	$3.32238$	$[0, 0, 0, 4200, 394000]$	$y^2=x^3+4200x+394000$	38.2.0.a.1	$[]$
178752.bt1	178752ds1	178752.bt	178752ds	$1$	$1$	$ 2^{6} \cdot 3 \cdot 7^{2} \cdot 19 $	$ - 2^{6} \cdot 3^{4} \cdot 7^{6} \cdot 19 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$38$	$2$	$0$	$1$	$1$	$0$	$96768$	$0.612407$	$175616/1539$	$0.88880$	$2.52689$	$[0, -1, 0, 229, 4929]$	$y^2=x^3-x^2+229x+4929$	38.2.0.a.1	$[]$
178752.hh1	178752bb1	178752.hh	178752bb	$1$	$1$	$ 2^{6} \cdot 3 \cdot 7^{2} \cdot 19 $	$ - 2^{6} \cdot 3^{4} \cdot 7^{6} \cdot 19 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$38$	$2$	$0$	$1$	$1$	$0$	$96768$	$0.612407$	$175616/1539$	$0.88880$	$2.52689$	$[0, 1, 0, 229, -4929]$	$y^2=x^3+x^2+229x-4929$	38.2.0.a.1	$[]$
207936.cr1	207936y1	207936.cr	207936y	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 19^{2} $	$ - 2^{6} \cdot 3^{10} \cdot 19^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$38$	$2$	$0$	$1$	$1$	$0$	$737280$	$1.660976$	$175616/1539$	$0.88880$	$3.52328$	$[0, 0, 0, 15162, -2702446]$	$y^2=x^3+15162x-2702446$	38.2.0.a.1	$[]$
207936.cx1	207936bb1	207936.cx	207936bb	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 19^{2} $	$ - 2^{6} \cdot 3^{10} \cdot 19^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$38$	$2$	$0$	$1$	$1$	$0$	$737280$	$1.660976$	$175616/1539$	$0.88880$	$3.52328$	$[0, 0, 0, 15162, 2702446]$	$y^2=x^3+15162x+2702446$	38.2.0.a.1	$[]$
220704.h1	220704bz1	220704.h	220704bz	$1$	$1$	$ 2^{5} \cdot 3 \cdot 11^{2} \cdot 19 $	$ - 2^{12} \cdot 3^{4} \cdot 11^{6} \cdot 19 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$38$	$2$	$0$	$1$	$1$	$0$	$345600$	$1.184973$	$175616/1539$	$0.88880$	$3.04199$	$[0, -1, 0, 2259, 154629]$	$y^2=x^3-x^2+2259x+154629$	38.2.0.a.1	$[]$
220704.bl1	220704bj1	220704.bl	220704bj	$1$	$1$	$ 2^{5} \cdot 3 \cdot 11^{2} \cdot 19 $	$ - 2^{12} \cdot 3^{4} \cdot 11^{6} \cdot 19 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$38$	$2$	$0$	$1$	$1$	$0$	$345600$	$1.184973$	$175616/1539$	$0.88880$	$3.04199$	$[0, 1, 0, 2259, -154629]$	$y^2=x^3+x^2+2259x-154629$	38.2.0.a.1	$[]$
268128.bd1	268128bd1	268128.bd	268128bd	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 7^{2} \cdot 19 $	$ - 2^{12} \cdot 3^{10} \cdot 7^{6} \cdot 19 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$38$	$2$	$0$	$3.885219722$	$1$	$2$	$774144$	$1.508286$	$175616/1539$	$0.88880$	$3.30502$	$[0, 0, 0, 8232, -1081136]$	$y^2=x^3+8232x-1081136$	38.2.0.a.1	$[(344, 6516)]$
268128.bj1	268128bj1	268128.bj	268128bj	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 7^{2} \cdot 19 $	$ - 2^{12} \cdot 3^{10} \cdot 7^{6} \cdot 19 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$38$	$2$	$0$	$1$	$1$	$0$	$774144$	$1.508286$	$175616/1539$	$0.88880$	$3.30502$	$[0, 0, 0, 8232, 1081136]$	$y^2=x^3+8232x+1081136$	38.2.0.a.1	$[]$
273600.fv1	273600fv1	273600.fv	273600fv	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 19 $	$ - 2^{6} \cdot 3^{10} \cdot 5^{6} \cdot 19 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$38$	$2$	$0$	$1$	$1$	$0$	$286720$	$0.993477$	$175616/1539$	$0.88880$	$2.80624$	$[0, 0, 0, 1050, -49250]$	$y^2=x^3+1050x-49250$	38.2.0.a.1	$[]$
273600.ks1	273600ks1	273600.ks	273600ks	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 19 $	$ - 2^{6} \cdot 3^{10} \cdot 5^{6} \cdot 19 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$38$	$2$	$0$	$6.740128715$	$1$	$0$	$286720$	$0.993477$	$175616/1539$	$0.88880$	$2.80624$	$[0, 0, 0, 1050, 49250]$	$y^2=x^3+1050x+49250$	38.2.0.a.1	$[(1741/5, 84789/5)]$
308256.v1	308256v1	308256.v	308256v	$1$	$1$	$ 2^{5} \cdot 3 \cdot 13^{2} \cdot 19 $	$ - 2^{12} \cdot 3^{4} \cdot 13^{6} \cdot 19 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$38$	$2$	$0$	$2.352792303$	$1$	$0$	$602112$	$1.268499$	$175616/1539$	$0.88880$	$3.04088$	$[0, -1, 0, 3155, -257531]$	$y^2=x^3-x^2+3155x-257531$	38.2.0.a.1	$[(205/2, 1521/2)]$
308256.cg1	308256cg1	308256.cg	308256cg	$1$	$1$	$ 2^{5} \cdot 3 \cdot 13^{2} \cdot 19 $	$ - 2^{12} \cdot 3^{4} \cdot 13^{6} \cdot 19 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$38$	$2$	$0$	$1.225571874$	$1$	$4$	$602112$	$1.268499$	$175616/1539$	$0.88880$	$3.04088$	$[0, 1, 0, 3155, 257531]$	$y^2=x^3+x^2+3155x+257531$	38.2.0.a.1	$[(329, 6084)]$
441408.cq1	441408cq1	441408.cq	441408cq	$1$	$1$	$ 2^{6} \cdot 3 \cdot 11^{2} \cdot 19 $	$ - 2^{6} \cdot 3^{4} \cdot 11^{6} \cdot 19 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$38$	$2$	$0$	$6.284337443$	$1$	$0$	$345600$	$0.838399$	$175616/1539$	$0.88880$	$2.55980$	$[0, -1, 0, 565, -19611]$	$y^2=x^3-x^2+565x-19611$	38.2.0.a.1	$[(1124/5, 38457/5)]$
441408.gs1	441408gs1	441408.gs	441408gs	$1$	$1$	$ 2^{6} \cdot 3 \cdot 11^{2} \cdot 19 $	$ - 2^{6} \cdot 3^{4} \cdot 11^{6} \cdot 19 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$38$	$2$	$0$	$4.770991032$	$1$	$2$	$345600$	$0.838399$	$175616/1539$	$0.88880$	$2.55980$	$[0, 1, 0, 565, 19611]$	$y^2=x^3+x^2+565x+19611$	38.2.0.a.1	$[(250, 3981)]$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

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