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

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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	$Ш_{\textrm{an}}$	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
5544.i1	5544c1	5544.i	5544c	$1$	$1$	$ 2^{3} \cdot 3^{2} \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{3} \cdot 7 \cdot 11 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$0.609243019$	$1$	$4$	$256$	$-0.450313$	$-6912/77$	$0.71623$	$2.07849$	$[0, 0, 0, -3, -9]$	$y^2=x^3-3x-9$	462.2.0.?	$[(3, 3)]$
5544.n1	5544l1	5544.n	5544l	$1$	$1$	$ 2^{3} \cdot 3^{2} \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{9} \cdot 7 \cdot 11 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$0.584578146$	$1$	$4$	$768$	$0.098994$	$-6912/77$	$0.71623$	$2.84315$	$[0, 0, 0, -27, 243]$	$y^2=x^3-27x+243$	462.2.0.?	$[(9, 27)]$
11088.p1	11088a1	11088.p	11088a	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{3} \cdot 7 \cdot 11 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$0.640703944$	$1$	$4$	$512$	$-0.450313$	$-6912/77$	$0.71623$	$1.92381$	$[0, 0, 0, -3, 9]$	$y^2=x^3-3x+9$	462.2.0.?	$[(0, 3)]$
11088.bc1	11088d1	11088.bc	11088d	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{9} \cdot 7 \cdot 11 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$1$	$1$	$0$	$1536$	$0.098994$	$-6912/77$	$0.71623$	$2.63155$	$[0, 0, 0, -27, -243]$	$y^2=x^3-27x-243$	462.2.0.?	$[]$
38808.ba1	38808bm1	38808.ba	38808bm	$1$	$1$	$ 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{4} \cdot 3^{9} \cdot 7^{7} \cdot 11 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$0.973917413$	$1$	$2$	$36864$	$1.071949$	$-6912/77$	$0.71623$	$3.42451$	$[0, 0, 0, -1323, -83349]$	$y^2=x^3-1323x-83349$	462.2.0.?	$[(126, 1323)]$
38808.bv1	38808k1	38808.bv	38808k	$1$	$1$	$ 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{4} \cdot 3^{3} \cdot 7^{7} \cdot 11 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$0.339063687$	$1$	$4$	$12288$	$0.522642$	$-6912/77$	$0.71623$	$2.80068$	$[0, 0, 0, -147, 3087]$	$y^2=x^3-147x+3087$	462.2.0.?	$[(7, 49)]$
44352.bw1	44352cu1	44352.bw	44352cu	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11 $	$ - 2^{10} \cdot 3^{9} \cdot 7 \cdot 11 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$1$	$1$	$0$	$12288$	$0.445567$	$-6912/77$	$0.71623$	$2.67929$	$[0, 0, 0, -108, -1944]$	$y^2=x^3-108x-1944$	462.2.0.?	$[]$
44352.co1	44352k1	44352.co	44352k	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11 $	$ - 2^{10} \cdot 3^{9} \cdot 7 \cdot 11 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$2.308031050$	$1$	$2$	$12288$	$0.445567$	$-6912/77$	$0.71623$	$2.67929$	$[0, 0, 0, -108, 1944]$	$y^2=x^3-108x+1944$	462.2.0.?	$[(45, 297)]$
44352.dk1	44352cy1	44352.dk	44352cy	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11 $	$ - 2^{10} \cdot 3^{3} \cdot 7 \cdot 11 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$1.456092593$	$1$	$2$	$4096$	$-0.103739$	$-6912/77$	$0.71623$	$2.06324$	$[0, 0, 0, -12, 72]$	$y^2=x^3-12x+72$	462.2.0.?	$[(-3, 9)]$
44352.dn1	44352g1	44352.dn	44352g	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11 $	$ - 2^{10} \cdot 3^{3} \cdot 7 \cdot 11 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$1$	$1$	$0$	$4096$	$-0.103739$	$-6912/77$	$0.71623$	$2.06324$	$[0, 0, 0, -12, -72]$	$y^2=x^3-12x-72$	462.2.0.?	$[]$
60984.v1	60984bl1	60984.v	60984bl	$1$	$1$	$ 2^{3} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{4} \cdot 3^{3} \cdot 7 \cdot 11^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$0.322141370$	$1$	$4$	$30720$	$0.748635$	$-6912/77$	$0.71623$	$2.93192$	$[0, 0, 0, -363, 11979]$	$y^2=x^3-363x+11979$	462.2.0.?	$[(-11, 121)]$
60984.bo1	60984c1	60984.bo	60984c	$1$	$1$	$ 2^{3} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{4} \cdot 3^{9} \cdot 7 \cdot 11^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$1$	$1$	$0$	$92160$	$1.297941$	$-6912/77$	$0.71623$	$3.53016$	$[0, 0, 0, -3267, -323433]$	$y^2=x^3-3267x-323433$	462.2.0.?	$[]$
77616.cu1	77616t1	77616.cu	77616t	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{4} \cdot 3^{9} \cdot 7^{7} \cdot 11 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$2.029519706$	$1$	$2$	$73728$	$1.071949$	$-6912/77$	$0.71623$	$3.21370$	$[0, 0, 0, -1323, 83349]$	$y^2=x^3-1323x+83349$	462.2.0.?	$[(252, 3969)]$
77616.ej1	77616f1	77616.ej	77616f	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{4} \cdot 3^{3} \cdot 7^{7} \cdot 11 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$1$	$1$	$0$	$24576$	$0.522642$	$-6912/77$	$0.71623$	$2.62827$	$[0, 0, 0, -147, -3087]$	$y^2=x^3-147x-3087$	462.2.0.?	$[]$
121968.cr1	121968r1	121968.cr	121968r	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{4} \cdot 3^{3} \cdot 7 \cdot 11^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$3.411192671$	$1$	$2$	$61440$	$0.748635$	$-6912/77$	$0.71623$	$2.75839$	$[0, 0, 0, -363, -11979]$	$y^2=x^3-363x-11979$	462.2.0.?	$[(36, 147)]$
121968.ej1	121968o1	121968.ej	121968o	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{4} \cdot 3^{9} \cdot 7 \cdot 11^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$1.913944557$	$1$	$2$	$184320$	$1.297941$	$-6912/77$	$0.71623$	$3.32123$	$[0, 0, 0, -3267, 323433]$	$y^2=x^3-3267x+323433$	462.2.0.?	$[(88, 847)]$
138600.r1	138600ey1	138600.r	138600ey	$1$	$1$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{9} \cdot 5^{6} \cdot 7 \cdot 11 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$1.947742666$	$1$	$2$	$107520$	$0.903712$	$-6912/77$	$0.71623$	$2.88579$	$[0, 0, 0, -675, 30375]$	$y^2=x^3-675x+30375$	462.2.0.?	$[(-9, 189)]$
138600.cd1	138600cj1	138600.cd	138600cj	$1$	$1$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{3} \cdot 5^{6} \cdot 7 \cdot 11 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$2.450823301$	$1$	$2$	$35840$	$0.354406$	$-6912/77$	$0.71623$	$2.32903$	$[0, 0, 0, -75, -1125]$	$y^2=x^3-75x-1125$	462.2.0.?	$[(21, 81)]$
277200.jh1	277200jh1	277200.jh	277200jh	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{3} \cdot 5^{6} \cdot 7 \cdot 11 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$1$	$1$	$0$	$71680$	$0.354406$	$-6912/77$	$0.71623$	$2.20022$	$[0, 0, 0, -75, 1125]$	$y^2=x^3-75x+1125$	462.2.0.?	$[]$
277200.mm1	277200mm1	277200.mm	277200mm	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{9} \cdot 5^{6} \cdot 7 \cdot 11 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$11.83643281$	$1$	$0$	$215040$	$0.903712$	$-6912/77$	$0.71623$	$2.72618$	$[0, 0, 0, -675, -30375]$	$y^2=x^3-675x-30375$	462.2.0.?	$[(697824/31, 582536907/31)]$
310464.ga1	310464ga1	310464.ga	310464ga	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{10} \cdot 3^{3} \cdot 7^{7} \cdot 11 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$2.073366230$	$1$	$6$	$196608$	$0.869216$	$-6912/77$	$0.71623$	$2.66902$	$[0, 0, 0, -588, 24696]$	$y^2=x^3-588x+24696$	462.2.0.?	$[(21, 147), (-35, 49)]$
310464.gv1	310464gv1	310464.gv	310464gv	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{10} \cdot 3^{3} \cdot 7^{7} \cdot 11 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$1$	$1$	$0$	$196608$	$0.869216$	$-6912/77$	$0.71623$	$2.66902$	$[0, 0, 0, -588, -24696]$	$y^2=x^3-588x-24696$	462.2.0.?	$[]$
310464.lc1	310464lc1	310464.lc	310464lc	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{10} \cdot 3^{9} \cdot 7^{7} \cdot 11 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$4.096584416$	$1$	$2$	$589824$	$1.418522$	$-6912/77$	$0.71623$	$3.19027$	$[0, 0, 0, -5292, 666792]$	$y^2=x^3-5292x+666792$	462.2.0.?	$[(261, 4131)]$
310464.lz1	310464lz1	310464.lz	310464lz	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{10} \cdot 3^{9} \cdot 7^{7} \cdot 11 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$5.011633454$	$1$	$0$	$589824$	$1.418522$	$-6912/77$	$0.71623$	$3.19027$	$[0, 0, 0, -5292, -666792]$	$y^2=x^3-5292x-666792$	462.2.0.?	$[(1141/3, 22589/3)]$
426888.ct1	426888ct1	426888.ct	426888ct	$1$	$1$	$ 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 11^{2} $	$ - 2^{4} \cdot 3^{9} \cdot 7^{7} \cdot 11^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$2.219795581$	$1$	$2$	$4423680$	$2.270897$	$-6912/77$	$0.71623$	$3.90088$	$[0, 0, 0, -160083, 110937519]$	$y^2=x^3-160083x+110937519$	462.2.0.?	$[(99, 9801)]$
426888.fd1	426888fd1	426888.fd	426888fd	$1$	$1$	$ 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 11^{2} $	$ - 2^{4} \cdot 3^{3} \cdot 7^{7} \cdot 11^{7} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$3.155508192$	$1$	$6$	$1474560$	$1.721590$	$-6912/77$	$0.71623$	$3.39243$	$[0, 0, 0, -17787, -4108797]$	$y^2=x^3-17787x-4108797$	462.2.0.?	$[(693, 17787), (198, 363)]$
487872.fq1	487872fq1	487872.fq	487872fq	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{10} \cdot 3^{9} \cdot 7 \cdot 11^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$1$	$1$	$0$	$1474560$	$1.644514$	$-6912/77$	$0.71623$	$3.28723$	$[0, 0, 0, -13068, -2587464]$	$y^2=x^3-13068x-2587464$	462.2.0.?	$[]$
487872.gv1	487872gv1	487872.gv	487872gv	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{10} \cdot 3^{9} \cdot 7 \cdot 11^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$1$	$1$	$0$	$1474560$	$1.644514$	$-6912/77$	$0.71623$	$3.28723$	$[0, 0, 0, -13068, 2587464]$	$y^2=x^3-13068x+2587464$	462.2.0.?	$[]$
487872.ke1	487872ke1	487872.ke	487872ke	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{10} \cdot 3^{3} \cdot 7 \cdot 11^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$1$	$1$	$0$	$491520$	$1.095209$	$-6912/77$	$0.71623$	$2.78397$	$[0, 0, 0, -1452, 95832]$	$y^2=x^3-1452x+95832$	462.2.0.?	$[]$
487872.lg1	487872lg1	487872.lg	487872lg	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{10} \cdot 3^{3} \cdot 7 \cdot 11^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$462$	$2$	$0$	$1$	$1$	$0$	$491520$	$1.095209$	$-6912/77$	$0.71623$	$2.78397$	$[0, 0, 0, -1452, -95832]$	$y^2=x^3-1452x-95832$	462.2.0.?	$[]$

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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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