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 (30 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	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
1550.b1	1550e1	1550.b	1550e	$1$	$1$	$ 2 \cdot 5^{2} \cdot 31 $	$ - 2^{11} \cdot 5^{4} \cdot 31 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$248$	$2$	$0$	$1$	$1$		$0$	$792$	$0.192349$	$-508660425/63488$	$0.99261$	$3.63195$	$[1, -1, 0, -142, -684]$	$y^2+xy=x^3-x^2-142x-684$	248.2.0.?	$[]$
1550.g1	1550f1	1550.g	1550f	$1$	$1$	$ 2 \cdot 5^{2} \cdot 31 $	$ - 2^{11} \cdot 5^{10} \cdot 31 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$248$	$2$	$0$	$1$	$1$		$0$	$3960$	$0.997067$	$-508660425/63488$	$0.99261$	$4.94649$	$[1, -1, 1, -3555, -89053]$	$y^2+xy+y=x^3-x^2-3555x-89053$	248.2.0.?	$[]$
12400.l1	12400u1	12400.l	12400u	$1$	$1$	$ 2^{4} \cdot 5^{2} \cdot 31 $	$ - 2^{23} \cdot 5^{10} \cdot 31 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$248$	$2$	$0$	$1.878658652$	$1$		$2$	$95040$	$1.690214$	$-508660425/63488$	$0.99261$	$4.73768$	$[0, 0, 0, -56875, 5756250]$	$y^2=x^3-56875x+5756250$	248.2.0.?	$[(149, 768)]$
12400.u1	12400bb1	12400.u	12400bb	$1$	$1$	$ 2^{4} \cdot 5^{2} \cdot 31 $	$ - 2^{23} \cdot 5^{4} \cdot 31 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$248$	$2$	$0$	$1$	$1$		$0$	$19008$	$0.885496$	$-508660425/63488$	$0.99261$	$3.71315$	$[0, 0, 0, -2275, 46050]$	$y^2=x^3-2275x+46050$	248.2.0.?	$[]$
13950.bn1	13950s1	13950.bn	13950s	$1$	$1$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{11} \cdot 3^{6} \cdot 5^{10} \cdot 31 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$248$	$2$	$0$	$1$	$1$		$0$	$126720$	$1.546373$	$-508660425/63488$	$0.99261$	$4.49833$	$[1, -1, 0, -31992, 2436416]$	$y^2+xy=x^3-x^2-31992x+2436416$	248.2.0.?	$[]$
13950.bq1	13950cv1	13950.bq	13950cv	$1$	$1$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{11} \cdot 3^{6} \cdot 5^{4} \cdot 31 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$248$	$2$	$0$	$0.054510982$	$1$		$42$	$25344$	$0.741655$	$-508660425/63488$	$0.99261$	$3.48645$	$[1, -1, 1, -1280, 19747]$	$y^2+xy+y=x^3-x^2-1280x+19747$	248.2.0.?	$[(-11, 185), (19, 35)]$
48050.g1	48050k1	48050.g	48050k	$1$	$1$	$ 2 \cdot 5^{2} \cdot 31^{2} $	$ - 2^{11} \cdot 5^{4} \cdot 31^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$248$	$2$	$0$	$1.308081340$	$1$		$2$	$760320$	$1.909342$	$-508660425/63488$	$0.99261$	$4.38630$	$[1, -1, 0, -136642, 21469716]$	$y^2+xy=x^3-x^2-136642x+21469716$	248.2.0.?	$[(225, 1329)]$
48050.t1	48050t1	48050.t	48050t	$1$	$1$	$ 2 \cdot 5^{2} \cdot 31^{2} $	$ - 2^{11} \cdot 5^{10} \cdot 31^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$248$	$2$	$0$	$1.334039812$	$1$		$2$	$3801600$	$2.714062$	$-508660425/63488$	$0.99261$	$5.28209$	$[1, -1, 1, -3416055, 2680298447]$	$y^2+xy+y=x^3-x^2-3416055x+2680298447$	248.2.0.?	$[(163, 46046)]$
49600.y1	49600bd1	49600.y	49600bd	$1$	$1$	$ 2^{6} \cdot 5^{2} \cdot 31 $	$ - 2^{29} \cdot 5^{4} \cdot 31 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$248$	$2$	$0$	$1$	$1$		$0$	$152064$	$1.232069$	$-508660425/63488$	$0.99261$	$3.62171$	$[0, 0, 0, -9100, -368400]$	$y^2=x^3-9100x-368400$	248.2.0.?	$[]$
49600.z1	49600cc1	49600.z	49600cc	$1$	$1$	$ 2^{6} \cdot 5^{2} \cdot 31 $	$ - 2^{29} \cdot 5^{10} \cdot 31 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$248$	$2$	$0$	$2.474244856$	$1$		$2$	$760320$	$2.036789$	$-508660425/63488$	$0.99261$	$4.51487$	$[0, 0, 0, -227500, 46050000]$	$y^2=x^3-227500x+46050000$	248.2.0.?	$[(-214, 9216)]$
49600.by1	49600f1	49600.by	49600f	$1$	$1$	$ 2^{6} \cdot 5^{2} \cdot 31 $	$ - 2^{29} \cdot 5^{10} \cdot 31 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$248$	$2$	$0$	$12.65610743$	$1$		$0$	$760320$	$2.036789$	$-508660425/63488$	$0.99261$	$4.51487$	$[0, 0, 0, -227500, -46050000]$	$y^2=x^3-227500x-46050000$	248.2.0.?	$[(12345046/127, 30944326656/127)]$
49600.bz1	49600cu1	49600.bz	49600cu	$1$	$1$	$ 2^{6} \cdot 5^{2} \cdot 31 $	$ - 2^{29} \cdot 5^{4} \cdot 31 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$248$	$2$	$0$	$1$	$1$		$0$	$152064$	$1.232069$	$-508660425/63488$	$0.99261$	$3.62171$	$[0, 0, 0, -9100, 368400]$	$y^2=x^3-9100x+368400$	248.2.0.?	$[]$
75950.bb1	75950br1	75950.bb	75950br	$1$	$1$	$ 2 \cdot 5^{2} \cdot 7^{2} \cdot 31 $	$ - 2^{11} \cdot 5^{4} \cdot 7^{6} \cdot 31 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$248$	$2$	$0$	$1$	$1$		$0$	$185328$	$1.165304$	$-508660425/63488$	$0.99261$	$3.41310$	$[1, -1, 0, -6967, 248541]$	$y^2+xy=x^3-x^2-6967x+248541$	248.2.0.?	$[]$
75950.ct1	75950cn1	75950.ct	75950cn	$1$	$1$	$ 2 \cdot 5^{2} \cdot 7^{2} \cdot 31 $	$ - 2^{11} \cdot 5^{10} \cdot 7^{6} \cdot 31 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$248$	$2$	$0$	$1$	$1$		$0$	$926640$	$1.970022$	$-508660425/63488$	$0.99261$	$4.27239$	$[1, -1, 1, -174180, 30893447]$	$y^2+xy+y=x^3-x^2-174180x+30893447$	248.2.0.?	$[]$
111600.f1	111600fq1	111600.f	111600fq	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{23} \cdot 3^{6} \cdot 5^{10} \cdot 31 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$248$	$2$	$0$	$1$	$4$	$2$	$0$	$3041280$	$2.239521$	$-508660425/63488$	$0.99261$	$4.40917$	$[0, 0, 0, -511875, -155418750]$	$y^2=x^3-511875x-155418750$	248.2.0.?	$[]$
111600.gy1	111600gw1	111600.gy	111600gw	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{23} \cdot 3^{6} \cdot 5^{4} \cdot 31 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$248$	$2$	$0$	$0.948112599$	$1$		$4$	$608256$	$1.434803$	$-508660425/63488$	$0.99261$	$3.57833$	$[0, 0, 0, -20475, -1243350]$	$y^2=x^3-20475x-1243350$	248.2.0.?	$[(525, 11520)]$
187550.l1	187550bp1	187550.l	187550bp	$1$	$1$	$ 2 \cdot 5^{2} \cdot 11^{2} \cdot 31 $	$ - 2^{11} \cdot 5^{10} \cdot 11^{6} \cdot 31 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$248$	$2$	$0$	$1$	$1$		$0$	$4712400$	$2.196014$	$-508660425/63488$	$0.99261$	$4.17766$	$[1, -1, 0, -430117, 119819541]$	$y^2+xy=x^3-x^2-430117x+119819541$	248.2.0.?	$[]$
187550.bn1	187550m1	187550.bn	187550m	$1$	$1$	$ 2 \cdot 5^{2} \cdot 11^{2} \cdot 31 $	$ - 2^{11} \cdot 5^{4} \cdot 11^{6} \cdot 31 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$248$	$2$	$0$	$1$	$1$		$0$	$942480$	$1.391296$	$-508660425/63488$	$0.99261$	$3.38234$	$[1, -1, 1, -17205, 961997]$	$y^2+xy+y=x^3-x^2-17205x+961997$	248.2.0.?	$[]$
261950.j1	261950j1	261950.j	261950j	$1$	$1$	$ 2 \cdot 5^{2} \cdot 13^{2} \cdot 31 $	$ - 2^{11} \cdot 5^{10} \cdot 13^{6} \cdot 31 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$248$	$2$	$0$	$1$	$1$		$0$	$6985440$	$2.279541$	$-508660425/63488$	$0.99261$	$4.14612$	$[1, -1, 0, -600742, -197451084]$	$y^2+xy=x^3-x^2-600742x-197451084$	248.2.0.?	$[]$
261950.bq1	261950bq1	261950.bq	261950bq	$1$	$1$	$ 2 \cdot 5^{2} \cdot 13^{2} \cdot 31 $	$ - 2^{11} \cdot 5^{4} \cdot 13^{6} \cdot 31 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$248$	$2$	$0$	$1$	$1$		$0$	$1397088$	$1.474823$	$-508660425/63488$	$0.99261$	$3.37210$	$[1, -1, 1, -24030, -1574803]$	$y^2+xy+y=x^3-x^2-24030x-1574803$	248.2.0.?	$[]$
384400.bf1	384400bf1	384400.bf	384400bf	$1$	$1$	$ 2^{4} \cdot 5^{2} \cdot 31^{2} $	$ - 2^{23} \cdot 5^{10} \cdot 31^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$248$	$2$	$0$	$26.15740958$	$1$		$0$	$91238400$	$3.407207$	$-508660425/63488$	$0.99261$	$5.07477$	$[0, 0, 0, -54656875, -171484443750]$	$y^2=x^3-54656875x-171484443750$	248.2.0.?	$[(6049319598429/5155, 14870565334003406592/5155)]$
384400.bt1	384400bt1	384400.bt	384400bt	$1$	$1$	$ 2^{4} \cdot 5^{2} \cdot 31^{2} $	$ - 2^{23} \cdot 5^{4} \cdot 31^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$248$	$2$	$0$	$1$	$25$	$5$	$0$	$18247680$	$2.602489$	$-508660425/63488$	$0.99261$	$4.32383$	$[0, 0, 0, -2186275, -1371875550]$	$y^2=x^3-2186275x-1371875550$	248.2.0.?	$[]$
432450.eb1	432450eb1	432450.eb	432450eb	$1$	$1$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 31^{2} $	$ - 2^{11} \cdot 3^{6} \cdot 5^{10} \cdot 31^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$248$	$2$	$0$	$13.29057523$	$1$		$0$	$121651200$	$3.263367$	$-508660425/63488$	$0.99261$	$4.89570$	$[1, -1, 0, -30744492, -72337313584]$	$y^2+xy=x^3-x^2-30744492x-72337313584$	248.2.0.?	$[(1379515/11, 1362090794/11)]$
432450.eh1	432450eh1	432450.eh	432450eh	$1$	$1$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 31^{2} $	$ - 2^{11} \cdot 3^{6} \cdot 5^{4} \cdot 31^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$248$	$2$	$0$	$0.361047009$	$1$		$8$	$24330240$	$2.458649$	$-508660425/63488$	$0.99261$	$4.15158$	$[1, -1, 1, -1229780, -578452553]$	$y^2+xy+y=x^3-x^2-1229780x-578452553$	248.2.0.?	$[(2209, 85385)]$
446400.a1	446400a1	446400.a	446400a	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{29} \cdot 3^{6} \cdot 5^{10} \cdot 31 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$248$	$2$	$0$	$1$	$1$		$0$	$24330240$	$2.586094$	$-508660425/63488$	$0.99261$	$4.25901$	$[0, 0, 0, -2047500, -1243350000]$	$y^2=x^3-2047500x-1243350000$	248.2.0.?	$[]$
446400.o1	446400o1	446400.o	446400o	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{29} \cdot 3^{6} \cdot 5^{4} \cdot 31 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$248$	$2$	$0$	$1.168097082$	$1$		$4$	$4866048$	$1.781376$	$-508660425/63488$	$0.99261$	$3.51670$	$[0, 0, 0, -81900, 9946800]$	$y^2=x^3-81900x+9946800$	248.2.0.?	$[(486, 9216)]$
446400.tf1	446400tf1	446400.tf	446400tf	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{29} \cdot 3^{6} \cdot 5^{4} \cdot 31 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$248$	$2$	$0$	$4.432641921$	$1$		$2$	$4866048$	$1.781376$	$-508660425/63488$	$0.99261$	$3.51670$	$[0, 0, 0, -81900, -9946800]$	$y^2=x^3-81900x-9946800$	248.2.0.?	$[(336, 684)]$
446400.tt1	446400tt1	446400.tt	446400tt	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ - 2^{29} \cdot 3^{6} \cdot 5^{10} \cdot 31 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$248$	$2$	$0$	$1$	$4$	$2$	$0$	$24330240$	$2.586094$	$-508660425/63488$	$0.99261$	$4.25901$	$[0, 0, 0, -2047500, 1243350000]$	$y^2=x^3-2047500x+1243350000$	248.2.0.?	$[]$
447950.w1	447950w1	447950.w	447950w	$1$	$1$	$ 2 \cdot 5^{2} \cdot 17^{2} \cdot 31 $	$ - 2^{11} \cdot 5^{4} \cdot 17^{6} \cdot 31 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$248$	$2$	$0$	$3.513351133$	$1$		$0$	$3649536$	$1.608955$	$-508660425/63488$	$0.99261$	$3.35676$	$[1, -1, 0, -41092, -3524784]$	$y^2+xy=x^3-x^2-41092x-3524784$	248.2.0.?	$[(1191/2, 24819/2)]$
447950.bp1	447950bp1	447950.bp	447950bp	$1$	$1$	$ 2 \cdot 5^{2} \cdot 17^{2} \cdot 31 $	$ - 2^{11} \cdot 5^{10} \cdot 17^{6} \cdot 31 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$248$	$2$	$0$	$3.992328687$	$1$		$2$	$18247680$	$2.413673$	$-508660425/63488$	$0.99261$	$4.09887$	$[1, -1, 1, -1027305, -441625303]$	$y^2+xy+y=x^3-x^2-1027305x-441625303$	248.2.0.?	$[(3583, 202820)]$

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Elliptic curves over $\Q$
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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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