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 (28 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
6240.i1	6240w1	6240.i	6240w	$1$	$1$	$ 2^{5} \cdot 3 \cdot 5 \cdot 13 $	$ - 2^{12} \cdot 3^{3} \cdot 5 \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$390$	$2$	$0$	$0.737179270$	$1$	$4$	$1152$	$0.090411$	$-53157376/1755$	$0.82150$	$2.99380$	$[0, -1, 0, -125, 597]$	$y^2=x^3-x^2-125x+597$	390.2.0.?	$[(7, 4)]$
6240.bf1	6240o1	6240.bf	6240o	$1$	$1$	$ 2^{5} \cdot 3 \cdot 5 \cdot 13 $	$ - 2^{12} \cdot 3^{3} \cdot 5 \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$390$	$2$	$0$	$1.215415698$	$1$	$4$	$1152$	$0.090411$	$-53157376/1755$	$0.82150$	$2.99380$	$[0, 1, 0, -125, -597]$	$y^2=x^3+x^2-125x-597$	390.2.0.?	$[(13, 12)]$
12480.p1	12480g1	12480.p	12480g	$1$	$1$	$ 2^{6} \cdot 3 \cdot 5 \cdot 13 $	$ - 2^{6} \cdot 3^{3} \cdot 5 \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$390$	$2$	$0$	$1$	$1$	$0$	$1152$	$-0.256163$	$-53157376/1755$	$0.82150$	$2.33285$	$[0, -1, 0, -31, -59]$	$y^2=x^3-x^2-31x-59$	390.2.0.?	$[]$
12480.by1	12480z1	12480.by	12480z	$1$	$1$	$ 2^{6} \cdot 3 \cdot 5 \cdot 13 $	$ - 2^{6} \cdot 3^{3} \cdot 5 \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$390$	$2$	$0$	$0.518999184$	$1$	$4$	$1152$	$-0.256163$	$-53157376/1755$	$0.82150$	$2.33285$	$[0, 1, 0, -31, 59]$	$y^2=x^3+x^2-31x+59$	390.2.0.?	$[(2, 3)]$
18720.k1	18720f1	18720.k	18720f	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 13 $	$ - 2^{12} \cdot 3^{9} \cdot 5 \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$390$	$2$	$0$	$1$	$1$	$0$	$9216$	$0.639717$	$-53157376/1755$	$0.82150$	$3.32952$	$[0, 0, 0, -1128, -14992]$	$y^2=x^3-1128x-14992$	390.2.0.?	$[]$
18720.l1	18720ba1	18720.l	18720ba	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 13 $	$ - 2^{12} \cdot 3^{9} \cdot 5 \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$390$	$2$	$0$	$0.454718528$	$1$	$4$	$9216$	$0.639717$	$-53157376/1755$	$0.82150$	$3.32952$	$[0, 0, 0, -1128, 14992]$	$y^2=x^3-1128x+14992$	390.2.0.?	$[(32, 108)]$
31200.h1	31200bl1	31200.h	31200bl	$1$	$1$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 13 $	$ - 2^{12} \cdot 3^{3} \cdot 5^{7} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$390$	$2$	$0$	$1.884181068$	$1$	$2$	$27648$	$0.895130$	$-53157376/1755$	$0.82150$	$3.46135$	$[0, -1, 0, -3133, -68363]$	$y^2=x^3-x^2-3133x-68363$	390.2.0.?	$[(107, 900)]$
31200.cc1	31200q1	31200.cc	31200q	$1$	$1$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 13 $	$ - 2^{12} \cdot 3^{3} \cdot 5^{7} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$390$	$2$	$0$	$0.293967192$	$1$	$6$	$27648$	$0.895130$	$-53157376/1755$	$0.82150$	$3.46135$	$[0, 1, 0, -3133, 68363]$	$y^2=x^3+x^2-3133x+68363$	390.2.0.?	$[(-7, 300)]$
37440.ea1	37440co1	37440.ea	37440co	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13 $	$ - 2^{6} \cdot 3^{9} \cdot 5 \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$390$	$2$	$0$	$1$	$1$	$0$	$9216$	$0.293143$	$-53157376/1755$	$0.82150$	$2.71543$	$[0, 0, 0, -282, -1874]$	$y^2=x^3-282x-1874$	390.2.0.?	$[]$
37440.ev1	37440cn1	37440.ev	37440cn	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13 $	$ - 2^{6} \cdot 3^{9} \cdot 5 \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$390$	$2$	$0$	$1$	$1$	$0$	$9216$	$0.293143$	$-53157376/1755$	$0.82150$	$2.71543$	$[0, 0, 0, -282, 1874]$	$y^2=x^3-282x+1874$	390.2.0.?	$[]$
62400.dg1	62400d1	62400.dg	62400d	$1$	$1$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 13 $	$ - 2^{6} \cdot 3^{3} \cdot 5^{7} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$390$	$2$	$0$	$1.822480537$	$1$	$2$	$27648$	$0.548556$	$-53157376/1755$	$0.82150$	$2.86739$	$[0, -1, 0, -783, 8937]$	$y^2=x^3-x^2-783x+8937$	390.2.0.?	$[(32, 125)]$
62400.fb1	62400cg1	62400.fb	62400cg	$1$	$1$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 13 $	$ - 2^{6} \cdot 3^{3} \cdot 5^{7} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$390$	$2$	$0$	$1$	$1$	$0$	$27648$	$0.548556$	$-53157376/1755$	$0.82150$	$2.86739$	$[0, 1, 0, -783, -8937]$	$y^2=x^3+x^2-783x-8937$	390.2.0.?	$[]$
81120.k1	81120a1	81120.k	81120a	$1$	$1$	$ 2^{5} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{12} \cdot 3^{3} \cdot 5 \cdot 13^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$390$	$2$	$0$	$0.995653734$	$1$	$2$	$193536$	$1.372885$	$-53157376/1755$	$0.82150$	$3.67594$	$[0, -1, 0, -21181, 1226965]$	$y^2=x^3-x^2-21181x+1226965$	390.2.0.?	$[(191, 2028)]$
81120.bf1	81120bo1	81120.bf	81120bo	$1$	$1$	$ 2^{5} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{12} \cdot 3^{3} \cdot 5 \cdot 13^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$390$	$2$	$0$	$1.366986909$	$1$	$2$	$193536$	$1.372885$	$-53157376/1755$	$0.82150$	$3.67594$	$[0, 1, 0, -21181, -1226965]$	$y^2=x^3+x^2-21181x-1226965$	390.2.0.?	$[(485, 10140)]$
93600.ca1	93600bl1	93600.ca	93600bl	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{12} \cdot 3^{9} \cdot 5^{7} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$390$	$2$	$0$	$1.124834235$	$1$	$4$	$221184$	$1.444435$	$-53157376/1755$	$0.82150$	$3.70500$	$[0, 0, 0, -28200, 1874000]$	$y^2=x^3-28200x+1874000$	390.2.0.?	$[(40, 900)]$
93600.dd1	93600du1	93600.dd	93600du	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{12} \cdot 3^{9} \cdot 5^{7} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$390$	$2$	$0$	$1$	$1$	$0$	$221184$	$1.444435$	$-53157376/1755$	$0.82150$	$3.70500$	$[0, 0, 0, -28200, -1874000]$	$y^2=x^3-28200x-1874000$	390.2.0.?	$[]$
162240.cy1	162240gz1	162240.cy	162240gz	$1$	$1$	$ 2^{6} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{6} \cdot 3^{3} \cdot 5 \cdot 13^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$390$	$2$	$0$	$1$	$1$	$0$	$193536$	$1.026312$	$-53157376/1755$	$0.82150$	$3.11689$	$[0, -1, 0, -5295, -150723]$	$y^2=x^3-x^2-5295x-150723$	390.2.0.?	$[]$
162240.hm1	162240ff1	162240.hm	162240ff	$1$	$1$	$ 2^{6} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{6} \cdot 3^{3} \cdot 5 \cdot 13^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$390$	$2$	$0$	$1.889094953$	$1$	$2$	$193536$	$1.026312$	$-53157376/1755$	$0.82150$	$3.11689$	$[0, 1, 0, -5295, 150723]$	$y^2=x^3+x^2-5295x+150723$	390.2.0.?	$[(-22, 507)]$
187200.gk1	187200ly1	187200.gk	187200ly	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{6} \cdot 3^{9} \cdot 5^{7} \cdot 13 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$390$	$2$	$0$	$0.971653203$	$1$	$6$	$221184$	$1.097862$	$-53157376/1755$	$0.82150$	$3.15088$	$[0, 0, 0, -7050, 234250]$	$y^2=x^3-7050x+234250$	390.2.0.?	$[(65, 225), (185/2, 675/2)]$
187200.kd1	187200na1	187200.kd	187200na	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{6} \cdot 3^{9} \cdot 5^{7} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$390$	$2$	$0$	$1$	$1$	$0$	$221184$	$1.097862$	$-53157376/1755$	$0.82150$	$3.15088$	$[0, 0, 0, -7050, -234250]$	$y^2=x^3-7050x-234250$	390.2.0.?	$[]$
243360.dx1	243360dx1	243360.dx	243360dx	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{12} \cdot 3^{9} \cdot 5 \cdot 13^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$390$	$2$	$0$	$0.788626354$	$1$	$2$	$1548288$	$1.922192$	$-53157376/1755$	$0.82150$	$3.88181$	$[0, 0, 0, -190632, 32937424]$	$y^2=x^3-190632x+32937424$	390.2.0.?	$[(65, 4563)]$
243360.eg1	243360eg1	243360.eg	243360eg	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{12} \cdot 3^{9} \cdot 5 \cdot 13^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$390$	$2$	$0$	$1$	$1$	$0$	$1548288$	$1.922192$	$-53157376/1755$	$0.82150$	$3.88181$	$[0, 0, 0, -190632, -32937424]$	$y^2=x^3-190632x-32937424$	390.2.0.?	$[]$
305760.bg1	305760bg1	305760.bg	305760bg	$1$	$1$	$ 2^{5} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13 $	$ - 2^{12} \cdot 3^{3} \cdot 5 \cdot 7^{6} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$390$	$2$	$0$	$3.729915618$	$1$	$2$	$435456$	$1.063366$	$-53157376/1755$	$0.82150$	$2.99571$	$[0, -1, 0, -6141, 192501]$	$y^2=x^3-x^2-6141x+192501$	390.2.0.?	$[(-61, 580)]$
305760.eq1	305760eq1	305760.eq	305760eq	$1$	$1$	$ 2^{5} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13 $	$ - 2^{12} \cdot 3^{3} \cdot 5 \cdot 7^{6} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$390$	$2$	$0$	$6.423524614$	$1$	$2$	$435456$	$1.063366$	$-53157376/1755$	$0.82150$	$2.99571$	$[0, 1, 0, -6141, -192501]$	$y^2=x^3+x^2-6141x-192501$	390.2.0.?	$[(1697, 69852)]$
405600.ch1	405600ch1	405600.ch	405600ch	$1$	$1$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ - 2^{12} \cdot 3^{3} \cdot 5^{7} \cdot 13^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$390$	$2$	$0$	$11.54767298$	$1$	$0$	$4644864$	$2.177605$	$-53157376/1755$	$0.82150$	$3.96560$	$[0, -1, 0, -529533, -152311563]$	$y^2=x^3-x^2-529533x-152311563$	390.2.0.?	$[(14017787/109, 38064360100/109)]$
405600.ey1	405600ey1	405600.ey	405600ey	$1$	$1$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ - 2^{12} \cdot 3^{3} \cdot 5^{7} \cdot 13^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$390$	$2$	$0$	$1.359531941$	$1$	$4$	$4644864$	$2.177605$	$-53157376/1755$	$0.82150$	$3.96560$	$[0, 1, 0, -529533, 152311563]$	$y^2=x^3+x^2-529533x+152311563$	390.2.0.?	$[(1473, 50700)]$
486720.cz1	486720cz1	486720.cz	486720cz	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{6} \cdot 3^{9} \cdot 5 \cdot 13^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$390$	$2$	$0$	$1$	$1$	$0$	$1548288$	$1.575619$	$-53157376/1755$	$0.82150$	$3.35876$	$[0, 0, 0, -47658, 4117178]$	$y^2=x^3-47658x+4117178$	390.2.0.?	$[]$
486720.fm1	486720fm1	486720.fm	486720fm	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{6} \cdot 3^{9} \cdot 5 \cdot 13^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$390$	$2$	$0$	$1$	$1$	$0$	$1548288$	$1.575619$	$-53157376/1755$	$0.82150$	$3.35876$	$[0, 0, 0, -47658, -4117178]$	$y^2=x^3-47658x-4117178$	390.2.0.?	$[]$

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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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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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