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	Manin constant

Intrinsic torsion order

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Results (24 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	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	Intrinsic torsion order	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators	Manin constant
4275.d1	4275d2	4275.d	4275d	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 19 $	$ 3^{3} \cdot 5^{3} \cdot 19 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$0.770266764$	$1$		$4$	$1024$	$0.323141$	$115003963647/19$	$1.06999$	$4.01797$	$1$	$[1, -1, 1, -1520, 23182]$	$y^2+xy+y=x^3-x^2-1520x+23182$	2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 570.6.0.?, 1140.12.0.?	$[(19, 20)]$	$1$
4275.g1	4275c2	4275.g	4275c	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 19 $	$ 3^{9} \cdot 5^{9} \cdot 19 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$12.74496912$	$1$		$0$	$15360$	$1.677166$	$115003963647/19$	$1.06999$	$5.96142$	$1$	$[1, -1, 1, -341930, -76872428]$	$y^2+xy+y=x^3-x^2-341930x-76872428$	2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 570.6.0.?, 1140.12.0.?	$[(302003/11, 159236060/11)]$	$1$
4275.k1	4275b2	4275.k	4275b	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 19 $	$ 3^{9} \cdot 5^{3} \cdot 19 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$9.608092465$	$1$		$0$	$3072$	$0.872447$	$115003963647/19$	$1.06999$	$4.80640$	$1$	$[1, -1, 0, -13677, -612244]$	$y^2+xy=x^3-x^2-13677x-612244$	2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 570.6.0.?, 1140.12.0.?	$[(12463/6, 1259593/6)]$	$1$
4275.n1	4275a2	4275.n	4275a	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 19 $	$ 3^{3} \cdot 5^{9} \cdot 19 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$3.681226927$	$1$		$0$	$5120$	$1.127859$	$115003963647/19$	$1.06999$	$5.17299$	$1$	$[1, -1, 0, -37992, 2859791]$	$y^2+xy=x^3-x^2-37992x+2859791$	2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 570.6.0.?, 1140.12.0.?	$[(455/2, -313/2)]$	$1$
68400.bj1	68400dw2	68400.bj	68400dw	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 19 $	$ 2^{12} \cdot 3^{9} \cdot 5^{9} \cdot 19 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$3.402460688$	$1$		$5$	$983040$	$2.370312$	$115003963647/19$	$1.06999$	$5.22391$	$1$	$[0, 0, 0, -5470875, 4925306250]$	$y^2=x^3-5470875x+4925306250$	2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 570.6.0.?, 1140.12.0.?	$[(1351, 26)]$	$1$
68400.bu1	68400dv2	68400.bu	68400dv	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 19 $	$ 2^{12} \cdot 3^{3} \cdot 5^{9} \cdot 19 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$8.761726320$	$1$		$1$	$327680$	$1.821007$	$115003963647/19$	$1.06999$	$4.63183$	$1$	$[0, 0, 0, -607875, -182418750]$	$y^2=x^3-607875x-182418750$	2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 570.6.0.?, 1140.12.0.?	$[(8719/3, 317078/3)]$	$1$
68400.eu1	68400du2	68400.eu	68400du	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 19 $	$ 2^{12} \cdot 3^{9} \cdot 5^{3} \cdot 19 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$2.183643558$	$1$		$5$	$196608$	$1.565594$	$115003963647/19$	$1.06999$	$4.35653$	$1$	$[0, 0, 0, -218835, 39402450]$	$y^2=x^3-218835x+39402450$	2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 570.6.0.?, 1140.12.0.?	$[(271, 26)]$	$1$
68400.fb1	68400dt2	68400.fb	68400dt	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 19 $	$ 2^{12} \cdot 3^{3} \cdot 5^{3} \cdot 19 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$4.973375595$	$1$		$3$	$65536$	$1.016287$	$115003963647/19$	$1.06999$	$3.76445$	$1$	$[0, 0, 0, -24315, -1459350]$	$y^2=x^3-24315x-1459350$	2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 570.6.0.?, 1140.12.0.?	$[(199, 1258)]$	$1$
81225.g1	81225n2	81225.g	81225n	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 19^{2} $	$ 3^{9} \cdot 5^{3} \cdot 19^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$5.130621062$	$1$		$2$	$1105920$	$2.344666$	$115003963647/19$	$1.06999$	$5.11728$	$1$	$[1, -1, 1, -4937465, 4224068812]$	$y^2+xy+y=x^3-x^2-4937465x+4224068812$	2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 570.6.0.?, 1140.12.0.?	$[(-371, 77675)]$	$1$
81225.l1	81225m2	81225.l	81225m	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 19^{2} $	$ 3^{3} \cdot 5^{9} \cdot 19^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$26.91006688$	$1$		$0$	$1843200$	$2.600079$	$115003963647/19$	$1.06999$	$5.38839$	$1$	$[1, -1, 1, -13715180, -19546730678]$	$y^2+xy+y=x^3-x^2-13715180x-19546730678$	2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 570.6.0.?, 1140.12.0.?	$[(6963622193735/32627, 14233243768263423238/32627)]$	$1$
81225.bg1	81225l2	81225.bg	81225l	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 19^{2} $	$ 3^{3} \cdot 5^{3} \cdot 19^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$14.72780798$	$1$		$0$	$368640$	$1.795361$	$115003963647/19$	$1.06999$	$4.53420$	$1$	$[1, -1, 0, -548607, -156264124]$	$y^2+xy=x^3-x^2-548607x-156264124$	2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 570.6.0.?, 1140.12.0.?	$[(34959359/170, 148385784387/170)]$	$1$
81225.bm1	81225k2	81225.bm	81225k	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 19^{2} $	$ 3^{9} \cdot 5^{9} \cdot 19^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$27.18441585$	$1$		$0$	$5529600$	$3.149384$	$115003963647/19$	$1.06999$	$5.97147$	$1$	$[1, -1, 0, -123436617, 527885164916]$	$y^2+xy=x^3-x^2-123436617x+527885164916$	2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 570.6.0.?, 1140.12.0.?	$[(22098594196175/47302, 54686035720739299893/47302)]$	$1$
209475.be1	209475bm2	209475.be	209475bm	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 19 $	$ 3^{3} \cdot 5^{3} \cdot 7^{6} \cdot 19 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$7.657374657$	$1$		$0$	$368640$	$1.296095$	$115003963647/19$	$1.06999$	$3.69462$	$1$	$[1, -1, 1, -74465, -7802588]$	$y^2+xy+y=x^3-x^2-74465x-7802588$	2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 570.6.0.?, 1140.12.0.?	$[(1487/2, 30295/2)]$	$1$
209475.bl1	209475bn2	209475.bl	209475bn	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 19 $	$ 3^{9} \cdot 5^{9} \cdot 7^{6} \cdot 19 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$8.827418169$	$1$		$0$	$5529600$	$2.650120$	$115003963647/19$	$1.06999$	$5.02076$	$1$	$[1, -1, 1, -16754555, 26400751822]$	$y^2+xy+y=x^3-x^2-16754555x+26400751822$	2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 570.6.0.?, 1140.12.0.?	$[(13547/2, 723793/2)]$	$1$
209475.de1	209475dk2	209475.de	209475dk	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 19 $	$ 3^{3} \cdot 5^{9} \cdot 7^{6} \cdot 19 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$30.58772218$	$1$		$0$	$1843200$	$2.100815$	$115003963647/19$	$1.06999$	$4.48277$	$1$	$[1, -1, 0, -1861617, -977185084]$	$y^2+xy=x^3-x^2-1861617x-977185084$	2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 570.6.0.?, 1140.12.0.?	$[(17481937948955/47174, 71492769253346931531/47174)]$	$1$
209475.dl1	209475dl2	209475.dl	209475dl	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 19 $	$ 3^{9} \cdot 5^{3} \cdot 7^{6} \cdot 19 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$6.445463388$	$1$		$0$	$1105920$	$1.845402$	$115003963647/19$	$1.06999$	$4.23261$	$1$	$[1, -1, 0, -670182, 211340051]$	$y^2+xy=x^3-x^2-670182x+211340051$	2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 570.6.0.?, 1140.12.0.?	$[(2147/2, 17517/2)]$	$1$
273600.du1	273600du2	273600.du	273600du	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 19 $	$ 2^{18} \cdot 3^{9} \cdot 5^{3} \cdot 19 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$1$	$4$	$2$	$1$	$1572864$	$1.912167$	$115003963647/19$	$1.06999$	$4.20632$	$1$	$[0, 0, 0, -875340, -315219600]$	$y^2=x^3-875340x-315219600$	2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 570.6.0.?, 1140.12.0.?	$[ ]$	$1$
273600.dx1	273600dx2	273600.dx	273600dx	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 19 $	$ 2^{18} \cdot 3^{3} \cdot 5^{9} \cdot 19 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$1$	$4$	$2$	$1$	$2621440$	$2.167580$	$115003963647/19$	$1.06999$	$4.45114$	$1$	$[0, 0, 0, -2431500, -1459350000]$	$y^2=x^3-2431500x-1459350000$	2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 570.6.0.?, 1140.12.0.?	$[ ]$	$1$
273600.ep1	273600ep2	273600.ep	273600ep	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 19 $	$ 2^{18} \cdot 3^{3} \cdot 5^{3} \cdot 19 $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$7.253775854$	$1$		$11$	$524288$	$1.362862$	$115003963647/19$	$1.06999$	$3.67980$	$1$	$[0, 0, 0, -97260, 11674800]$	$y^2=x^3-97260x+11674800$	2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 570.6.0.?, 1140.12.0.?	$[(184, 92), (196, 376)]$	$1$
273600.es1	273600es2	273600.es	273600es	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 19 $	$ 2^{18} \cdot 3^{9} \cdot 5^{9} \cdot 19 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$1$	$4$	$2$	$1$	$7864320$	$2.716885$	$115003963647/19$	$1.06999$	$4.97765$	$1$	$[0, 0, 0, -21883500, 39402450000]$	$y^2=x^3-21883500x+39402450000$	2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 570.6.0.?, 1140.12.0.?	$[ ]$	$1$
273600.lw1	273600lw2	273600.lw	273600lw	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 19 $	$ 2^{18} \cdot 3^{3} \cdot 5^{3} \cdot 19 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$1$	$4$	$2$	$1$	$524288$	$1.362862$	$115003963647/19$	$1.06999$	$3.67980$	$1$	$[0, 0, 0, -97260, -11674800]$	$y^2=x^3-97260x-11674800$	2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 570.6.0.?, 1140.12.0.?	$[ ]$	$1$
273600.lz1	273600lz2	273600.lz	273600lz	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 19 $	$ 2^{18} \cdot 3^{9} \cdot 5^{9} \cdot 19 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$1$	$16$	$2$	$1$	$7864320$	$2.716885$	$115003963647/19$	$1.06999$	$4.97765$	$1$	$[0, 0, 0, -21883500, -39402450000]$	$y^2=x^3-21883500x-39402450000$	2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 570.6.0.?, 1140.12.0.?	$[ ]$	$1$
273600.mp1	273600mp2	273600.mp	273600mp	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 19 $	$ 2^{18} \cdot 3^{9} \cdot 5^{3} \cdot 19 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$1$	$4$	$2$	$1$	$1572864$	$1.912167$	$115003963647/19$	$1.06999$	$4.20632$	$1$	$[0, 0, 0, -875340, 315219600]$	$y^2=x^3-875340x+315219600$	2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 570.6.0.?, 1140.12.0.?	$[ ]$	$1$
273600.ms1	273600ms2	273600.ms	273600ms	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 19 $	$ 2^{18} \cdot 3^{3} \cdot 5^{9} \cdot 19 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$1$	$4$	$2$	$1$	$2621440$	$2.167580$	$115003963647/19$	$1.06999$	$4.45114$	$1$	$[0, 0, 0, -2431500, 1459350000]$	$y^2=x^3-2431500x+1459350000$	2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 570.6.0.?, 1140.12.0.?	$[ ]$	$1$

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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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