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 (20 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	Semistable	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
2093.h1	2093f3	2093.h	2093f	$3$	$9$	$ 7 \cdot 13 \cdot 23 $	$ - 7^{4} \cdot 13 \cdot 23^{9} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	9.24.0.3	3B.1.2	$37674$	$144$	$3$	$22.15637950$	$1$		$0$	$69984$	$2.618320$	$-360675992659311050823073792/56219378022244619$	$1.03901$	$7.99728$	$[0, 1, 1, -14829659, -21985816061]$	$y^2+y=x^3+x^2-14829659x-21985816061$	3.8.0-3.a.1.1, 9.24.0-9.a.1.1, 63.72.0-63.e.2.2, 598.2.0.?, 1794.16.0.?, $\ldots$	$[(14674995661/1230, 1608233748263209/1230)]$
14651.h1	14651e3	14651.h	14651e	$3$	$9$	$ 7^{2} \cdot 13 \cdot 23 $	$ - 7^{10} \cdot 13 \cdot 23^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$3$	9.12.0.1	3B	$37674$	$144$	$3$	$1$	$1$		$0$	$3359232$	$3.591274$	$-360675992659311050823073792/56219378022244619$	$1.03901$	$7.59211$	$[0, -1, 1, -726653307, 7539681602235]$	$y^2+y=x^3-x^2-726653307x+7539681602235$	3.4.0.a.1, 9.12.0.a.1, 21.8.0-3.a.1.2, 63.72.0-63.e.2.3, 598.2.0.?, $\ldots$	$[]$
18837.e1	18837r3	18837.e	18837r	$3$	$9$	$ 3^{2} \cdot 7 \cdot 13 \cdot 23 $	$ - 3^{6} \cdot 7^{4} \cdot 13 \cdot 23^{9} $	$1$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$		$3$	9.24.0.1	3B.1.1	$37674$	$144$	$3$	$5.379701538$	$1$		$4$	$2099520$	$3.167625$	$-360675992659311050823073792/56219378022244619$	$1.03901$	$6.88182$	$[0, 0, 1, -133466934, 593483566707]$	$y^2+y=x^3-133466934x+593483566707$	3.8.0-3.a.1.2, 9.24.0-9.a.1.2, 63.72.0-63.e.2.4, 598.2.0.?, 1794.16.0.?, $\ldots$	$[(6849, 25434)]$
27209.i1	27209b3	27209.i	27209b	$3$	$9$	$ 7 \cdot 13^{2} \cdot 23 $	$ - 7^{4} \cdot 13^{7} \cdot 23^{9} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$3$	9.12.0.1	3B	$37674$	$144$	$3$	$38.79765877$	$1$		$0$	$11757312$	$3.900795$	$-360675992659311050823073792/56219378022244619$	$1.03901$	$7.49559$	$[0, 1, 1, -2506212427, -48292813035840]$	$y^2+y=x^3+x^2-2506212427x-48292813035840$	3.4.0.a.1, 9.12.0.a.1, 39.8.0-3.a.1.2, 63.36.0.e.2, 117.24.0.?, $\ldots$	$[(1172315329411772536/4455033, 276137919083904384973390552/4455033)]$
33488.m1	33488t3	33488.m	33488t	$3$	$9$	$ 2^{4} \cdot 7 \cdot 13 \cdot 23 $	$ - 2^{12} \cdot 7^{4} \cdot 13 \cdot 23^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$3$	9.12.0.1	3B	$75348$	$144$	$3$	$1$	$1$		$0$	$5038848$	$3.311466$	$-360675992659311050823073792/56219378022244619$	$1.03901$	$6.66745$	$[0, -1, 0, -237274549, 1406854953341]$	$y^2=x^3-x^2-237274549x+1406854953341$	3.4.0.a.1, 9.12.0.a.1, 12.8.0-3.a.1.2, 36.24.0-9.a.1.1, 63.36.0.e.2, $\ldots$	$[]$
48139.i1	48139f3	48139.i	48139f	$3$	$9$	$ 7 \cdot 13 \cdot 23^{2} $	$ - 7^{4} \cdot 13 \cdot 23^{15} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$3$	9.12.0.1	3B	$37674$	$144$	$3$	$9.467457489$	$1$		$0$	$36951552$	$4.186066$	$-360675992659311050823073792/56219378022244619$	$1.03901$	$7.41645$	$[0, 1, 1, -7844889787, 267438664893297]$	$y^2+y=x^3+x^2-7844889787x+267438664893297$	3.4.0.a.1, 9.12.0.a.1, 63.36.0.e.2, 69.8.0-3.a.1.1, 78.8.0.?, $\ldots$	$[(37243716337/852, 41440413423889/852)]$
52325.g1	52325d3	52325.g	52325d	$3$	$9$	$ 5^{2} \cdot 7 \cdot 13 \cdot 23 $	$ - 5^{6} \cdot 7^{4} \cdot 13 \cdot 23^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$3$	9.12.0.1	3B	$188370$	$144$	$3$	$1$	$1$		$0$	$7558272$	$3.423038$	$-360675992659311050823073792/56219378022244619$	$1.03901$	$6.51681$	$[0, -1, 1, -370741483, -2747485524632]$	$y^2+y=x^3-x^2-370741483x-2747485524632$	3.4.0.a.1, 9.12.0.a.1, 15.8.0-3.a.1.1, 45.24.0-9.a.1.2, 63.36.0.e.2, $\ldots$	$[]$
131859.w1	131859w3	131859.w	131859w	$3$	$9$	$ 3^{2} \cdot 7^{2} \cdot 13 \cdot 23 $	$ - 3^{6} \cdot 7^{10} \cdot 13 \cdot 23^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$3$	9.12.0.1	3B	$37674$	$144$	$3$	$1$	$9$	$3$	$0$	$100776960$	$4.140579$	$-360675992659311050823073792/56219378022244619$	$1.03901$	$6.73627$	$[0, 0, 1, -6539879766, -203564863380587]$	$y^2+y=x^3-6539879766x-203564863380587$	3.4.0.a.1, 9.12.0.a.1, 21.8.0-3.a.1.1, 63.72.0-63.e.2.1, 598.2.0.?, $\ldots$	$[]$
133952.t1	133952bz3	133952.t	133952bz	$3$	$9$	$ 2^{6} \cdot 7 \cdot 13 \cdot 23 $	$ - 2^{6} \cdot 7^{4} \cdot 13 \cdot 23^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$3$	9.12.0.1	3B	$150696$	$144$	$3$	$1$	$9$	$3$	$0$	$10077696$	$2.964893$	$-360675992659311050823073792/56219378022244619$	$1.03901$	$5.53220$	$[0, -1, 0, -59318637, -175827209849]$	$y^2=x^3-x^2-59318637x-175827209849$	3.4.0.a.1, 9.12.0.a.1, 24.8.0-3.a.1.1, 63.36.0.e.2, 72.24.0.?, $\ldots$	$[]$
133952.br1	133952x3	133952.br	133952x	$3$	$9$	$ 2^{6} \cdot 7 \cdot 13 \cdot 23 $	$ - 2^{6} \cdot 7^{4} \cdot 13 \cdot 23^{9} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$3$	9.12.0.1	3B	$150696$	$144$	$3$	$0.824442049$	$1$		$2$	$10077696$	$2.964893$	$-360675992659311050823073792/56219378022244619$	$1.03901$	$5.53220$	$[0, 1, 0, -59318637, 175827209849]$	$y^2=x^3+x^2-59318637x+175827209849$	3.4.0.a.1, 9.12.0.a.1, 24.8.0-3.a.1.3, 63.36.0.e.2, 72.24.0.?, $\ldots$	$[(4456, 1127)]$
190463.w1	190463w3	190463.w	190463w	$3$	$9$	$ 7^{2} \cdot 13^{2} \cdot 23 $	$ - 7^{10} \cdot 13^{7} \cdot 23^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$3$	9.12.0.1	3B	$37674$	$144$	$3$	$1$	$4$	$2$	$0$	$564350976$	$4.873749$	$-360675992659311050823073792/56219378022244619$	$1.03901$	$7.25620$	$[0, -1, 1, -122804408939, 16564189262475168]$	$y^2+y=x^3-x^2-122804408939x+16564189262475168$	3.4.0.a.1, 9.12.0.a.1, 63.36.0.e.2, 273.8.0.?, 598.2.0.?, $\ldots$	$[]$
234416.bj1	234416bj3	234416.bj	234416bj	$3$	$9$	$ 2^{4} \cdot 7^{2} \cdot 13 \cdot 23 $	$ - 2^{12} \cdot 7^{10} \cdot 13 \cdot 23^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$3$	9.12.0.1	3B	$75348$	$144$	$3$	$1$	$4$	$2$	$0$	$241864704$	$4.284424$	$-360675992659311050823073792/56219378022244619$	$1.03901$	$6.56241$	$[0, 1, 0, -11626452917, -482527996090141]$	$y^2=x^3+x^2-11626452917x-482527996090141$	3.4.0.a.1, 9.12.0.a.1, 63.36.0.e.2, 84.8.0.?, 252.72.0.?, $\ldots$	$[]$
244881.bk1	244881bk3	244881.bk	244881bk	$3$	$9$	$ 3^{2} \cdot 7 \cdot 13^{2} \cdot 23 $	$ - 3^{6} \cdot 7^{4} \cdot 13^{7} \cdot 23^{9} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$3$	9.12.0.1	3B	$37674$	$144$	$3$	$2.687542423$	$1$		$2$	$352719360$	$4.450104$	$-360675992659311050823073792/56219378022244619$	$1.03901$	$6.69954$	$[0, 0, 1, -22555911846, 1303883396055828]$	$y^2+y=x^3-22555911846x+1303883396055828$	3.4.0.a.1, 9.12.0.a.1, 39.8.0-3.a.1.1, 63.36.0.e.2, 117.24.0.?, $\ldots$	$[(87048, 172971)]$
253253.k1	253253k3	253253.k	253253k	$3$	$9$	$ 7 \cdot 11^{2} \cdot 13 \cdot 23 $	$ - 7^{4} \cdot 11^{6} \cdot 13 \cdot 23^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$3$	9.12.0.1	3B	$414414$	$144$	$3$	$1$	$25$	$5$	$0$	$94478400$	$3.817268$	$-360675992659311050823073792/56219378022244619$	$1.03901$	$6.07109$	$[0, 1, 1, -1794388779, 29255943621790]$	$y^2+y=x^3+x^2-1794388779x+29255943621790$	3.4.0.a.1, 9.12.0.a.1, 33.8.0-3.a.1.1, 63.36.0.e.2, 99.24.0.?, $\ldots$	$[]$
301392.j1	301392j3	301392.j	301392j	$3$	$9$	$ 2^{4} \cdot 3^{2} \cdot 7 \cdot 13 \cdot 23 $	$ - 2^{12} \cdot 3^{6} \cdot 7^{4} \cdot 13 \cdot 23^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$3$	9.12.0.1	3B	$75348$	$144$	$3$	$1$	$81$	$3$	$0$	$151165440$	$3.860775$	$-360675992659311050823073792/56219378022244619$	$1.03901$	$6.02873$	$[0, 0, 0, -2135470944, -37982948269264]$	$y^2=x^3-2135470944x-37982948269264$	3.4.0.a.1, 9.12.0.a.1, 12.8.0-3.a.1.1, 36.24.0-9.a.1.2, 63.36.0.e.2, $\ldots$	$[]$
336973.p1	336973p3	336973.p	336973p	$3$	$9$	$ 7^{2} \cdot 13 \cdot 23^{2} $	$ - 7^{10} \cdot 13 \cdot 23^{15} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$3$	9.12.0.1	3B	$37674$	$144$	$3$	$102.5753993$	$1$		$0$	$1773674496$	$5.159019$	$-360675992659311050823073792/56219378022244619$	$1.03901$	$7.19989$	$[0, -1, 1, -384399599579, -91732230857600103]$	$y^2+y=x^3-x^2-384399599579x-91732230857600103$	3.4.0.a.1, 9.12.0.a.1, 63.36.0.e.2, 483.8.0.?, 546.8.0.?, $\ldots$	$[(385594627075259503588859483248376002156877198221/185960340383623545990, 239061492187354955596610430788030804687682386836873840208259807548791181/185960340383623545990)]$
366275.r1	366275r3	366275.r	366275r	$3$	$9$	$ 5^{2} \cdot 7^{2} \cdot 13 \cdot 23 $	$ - 5^{6} \cdot 7^{10} \cdot 13 \cdot 23^{9} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$3$	9.12.0.1	3B	$188370$	$144$	$3$	$8.492636501$	$1$		$2$	$362797056$	$4.395996$	$-360675992659311050823073792/56219378022244619$	$1.03901$	$6.43831$	$[0, 1, 1, -18166332683, 942423867614044]$	$y^2+y=x^3+x^2-18166332683x+942423867614044$	3.4.0.a.1, 9.12.0.a.1, 63.36.0.e.2, 105.8.0.?, 315.72.0.?, $\ldots$	$[(310493/2, 751705/2), (1937804/5, 18416808/5)]$
433251.bb1	433251bb3	433251.bb	433251bb	$3$	$9$	$ 3^{2} \cdot 7 \cdot 13 \cdot 23^{2} $	$ - 3^{6} \cdot 7^{4} \cdot 13 \cdot 23^{15} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$3$	9.12.0.1	3B	$37674$	$144$	$3$	$1$	$81$	$3$	$0$	$1108546560$	$4.735374$	$-360675992659311050823073792/56219378022244619$	$1.03901$	$6.66879$	$[0, 0, 1, -70604008086, -7220914556127111]$	$y^2+y=x^3-70604008086x-7220914556127111$	3.4.0.a.1, 9.12.0.a.1, 63.36.0.e.2, 69.8.0-3.a.1.2, 78.8.0.?, $\ldots$	$[]$
435344.o1	435344o3	435344.o	435344o	$3$	$9$	$ 2^{4} \cdot 7 \cdot 13^{2} \cdot 23 $	$ - 2^{12} \cdot 7^{4} \cdot 13^{7} \cdot 23^{9} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$3$	9.12.0.1	3B	$75348$	$144$	$3$	$1.502044035$	$1$		$6$	$846526464$	$4.593941$	$-360675992659311050823073792/56219378022244619$	$1.03901$	$6.53560$	$[0, -1, 0, -40099398837, 3090699934894909]$	$y^2=x^3-x^2-40099398837x+3090699934894909$	3.4.0.a.1, 9.12.0.a.1, 63.36.0.e.2, 156.8.0.?, 276.8.0.?, $\ldots$	$[(1040692/3, 625807/3), (118924, 1958887)]$
470925.br1	470925br3	470925.br	470925br	$3$	$9$	$ 3^{2} \cdot 5^{2} \cdot 7 \cdot 13 \cdot 23 $	$ - 3^{6} \cdot 5^{6} \cdot 7^{4} \cdot 13 \cdot 23^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$3$	9.12.0.1	3B	$188370$	$144$	$3$	$1$	$1$		$0$	$226748160$	$3.972347$	$-360675992659311050823073792/56219378022244619$	$1.03901$	$5.92525$	$[0, 0, 1, -3336673350, 74185445838406]$	$y^2+y=x^3-3336673350x+74185445838406$	3.4.0.a.1, 9.12.0.a.1, 15.8.0-3.a.1.2, 45.24.0-9.a.1.1, 63.36.0.e.2, $\ldots$	$[]$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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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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