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.d2	4275d1	4275.d	4275d	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 19 $	$ - 3^{3} \cdot 5^{3} \cdot 19^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$0.385133382$	$1$		$9$	$512$	$-0.023433$	$-27818127/361$	$1.00533$	$3.02463$	$1$	$[1, -1, 1, -95, 382]$	$y^2+xy+y=x^3-x^2-95x+382$	2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.?	$[(4, 5)]$	$1$
4275.g2	4275c1	4275.g	4275c	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 19 $	$ - 3^{9} \cdot 5^{9} \cdot 19^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$6.372484561$	$1$		$3$	$7680$	$1.330591$	$-27818127/361$	$1.00533$	$4.96808$	$1$	$[1, -1, 1, -21305, -1204928]$	$y^2+xy+y=x^3-x^2-21305x-1204928$	2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.?	$[(2468, 121135)]$	$1$
4275.k2	4275b1	4275.k	4275b	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 19 $	$ - 3^{9} \cdot 5^{3} \cdot 19^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$4.804046232$	$1$		$1$	$1536$	$0.525873$	$-27818127/361$	$1.00533$	$3.81306$	$1$	$[1, -1, 0, -852, -9469]$	$y^2+xy=x^3-x^2-852x-9469$	2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.?	$[(382/3, 4063/3)]$	$1$
4275.n2	4275a1	4275.n	4275a	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 19 $	$ - 3^{3} \cdot 5^{9} \cdot 19^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$1.840613463$	$1$		$3$	$2560$	$0.781286$	$-27818127/361$	$1.00533$	$4.17965$	$1$	$[1, -1, 0, -2367, 45416]$	$y^2+xy=x^3-x^2-2367x+45416$	2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.?	$[(20, 66)]$	$1$
68400.bj2	68400dw1	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^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$1.701230344$	$1$		$7$	$491520$	$2.023739$	$-27818127/361$	$1.00533$	$4.47795$	$1$	$[0, 0, 0, -340875, 77456250]$	$y^2=x^3-340875x+77456250$	2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.?	$[(351, 1026)]$	$1$
68400.bu2	68400dv1	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^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$4.380863160$	$1$		$3$	$163840$	$1.474434$	$-27818127/361$	$1.00533$	$3.88587$	$1$	$[0, 0, 0, -37875, -2868750]$	$y^2=x^3-37875x-2868750$	2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.?	$[(441, 8136)]$	$1$
68400.eu2	68400du1	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^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$1.091821779$	$1$		$7$	$98304$	$1.219021$	$-27818127/361$	$1.00533$	$3.61057$	$1$	$[0, 0, 0, -13635, 619650]$	$y^2=x^3-13635x+619650$	2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.?	$[(81, 216)]$	$1$
68400.fb2	68400dt1	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^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$2.486687797$	$1$		$5$	$32768$	$0.669714$	$-27818127/361$	$1.00533$	$3.01850$	$1$	$[0, 0, 0, -1515, -22950]$	$y^2=x^3-1515x-22950$	2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.?	$[(85, 680)]$	$1$
81225.g2	81225n1	81225.g	81225n	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 19^{2} $	$ - 3^{9} \cdot 5^{3} \cdot 19^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$2.565310531$	$1$		$3$	$552960$	$1.998093$	$-27818127/361$	$1.00533$	$4.38266$	$1$	$[1, -1, 1, -307640, 66485962]$	$y^2+xy+y=x^3-x^2-307640x+66485962$	2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.?	$[(290, 1118)]$	$1$
81225.l2	81225m1	81225.l	81225m	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 19^{2} $	$ - 3^{3} \cdot 5^{9} \cdot 19^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$13.45503344$	$1$		$1$	$921600$	$2.253506$	$-27818127/361$	$1.00533$	$4.65377$	$1$	$[1, -1, 1, -854555, -307235678]$	$y^2+xy+y=x^3-x^2-854555x-307235678$	2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.?	$[(9912440/79, 23459439322/79)]$	$1$
81225.bg2	81225l1	81225.bg	81225l	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 19^{2} $	$ - 3^{3} \cdot 5^{3} \cdot 19^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$7.363903992$	$1$		$1$	$184320$	$1.448786$	$-27818127/361$	$1.00533$	$3.79958$	$1$	$[1, -1, 0, -34182, -2451049]$	$y^2+xy=x^3-x^2-34182x-2451049$	2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.?	$[(27314/5, 4374903/5)]$	$1$
81225.bm2	81225k1	81225.bm	81225k	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 19^{2} $	$ - 3^{9} \cdot 5^{9} \cdot 19^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$13.59220792$	$1$		$1$	$2764800$	$2.802811$	$-27818127/361$	$1.00533$	$5.23685$	$1$	$[1, -1, 0, -7690992, 8303054291]$	$y^2+xy=x^3-x^2-7690992x+8303054291$	2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.?	$[(-4921450/67, 37508344627/67)]$	$1$
209475.be2	209475bm1	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^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$3.828687328$	$1$		$3$	$184320$	$0.949522$	$-27818127/361$	$1.00533$	$3.01681$	$1$	$[1, -1, 1, -4640, -121838]$	$y^2+xy+y=x^3-x^2-4640x-121838$	2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.?	$[(139, 1310)]$	$1$
209475.bl2	209475bn1	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^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$4.413709084$	$1$		$3$	$2764800$	$2.303547$	$-27818127/361$	$1.00533$	$4.34294$	$1$	$[1, -1, 1, -1043930, 415378072]$	$y^2+xy+y=x^3-x^2-1043930x+415378072$	2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.?	$[(2543, 117896)]$	$1$
209475.de2	209475dk1	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^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$15.29386109$	$1$		$1$	$921600$	$1.754242$	$-27818127/361$	$1.00533$	$3.80495$	$1$	$[1, -1, 0, -115992, -15345709]$	$y^2+xy=x^3-x^2-115992x-15345709$	2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.?	$[(82841446/103, 748968022531/103)]$	$1$
209475.dl2	209475dl1	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^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$3.222731694$	$1$		$3$	$552960$	$1.498829$	$-27818127/361$	$1.00533$	$3.55480$	$1$	$[1, -1, 0, -41757, 3331376]$	$y^2+xy=x^3-x^2-41757x+3331376$	2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.?	$[(304, 4168)]$	$1$
273600.du2	273600du1	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^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$1$	$1$		$1$	$786432$	$1.565594$	$-27818127/361$	$1.00533$	$3.54296$	$1$	$[0, 0, 0, -54540, -4957200]$	$y^2=x^3-54540x-4957200$	2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.?	$[ ]$	$1$
273600.dx2	273600dx1	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^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$1$	$1$		$1$	$1310720$	$1.821007$	$-27818127/361$	$1.00533$	$3.78778$	$1$	$[0, 0, 0, -151500, -22950000]$	$y^2=x^3-151500x-22950000$	2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.?	$[ ]$	$1$
273600.ep2	273600ep1	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} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$1.813443963$	$1$		$17$	$262144$	$1.016287$	$-27818127/361$	$1.00533$	$3.01645$	$1$	$[0, 0, 0, -6060, 183600]$	$y^2=x^3-6060x+183600$	2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.?	$[(24, 228), (6, 384)]$	$1$
273600.es2	273600es1	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^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$1$	$1$		$1$	$3932160$	$2.370312$	$-27818127/361$	$1.00533$	$4.31429$	$1$	$[0, 0, 0, -1363500, 619650000]$	$y^2=x^3-1363500x+619650000$	2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.?	$[ ]$	$1$
273600.lw2	273600lw1	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^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$1$	$1$		$1$	$262144$	$1.016287$	$-27818127/361$	$1.00533$	$3.01645$	$1$	$[0, 0, 0, -6060, -183600]$	$y^2=x^3-6060x-183600$	2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.?	$[ ]$	$1$
273600.lz2	273600lz1	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^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$1$	$4$	$2$	$1$	$3932160$	$2.370312$	$-27818127/361$	$1.00533$	$4.31429$	$1$	$[0, 0, 0, -1363500, -619650000]$	$y^2=x^3-1363500x-619650000$	2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.?	$[ ]$	$1$
273600.mp2	273600mp1	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^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$1$	$1$		$1$	$786432$	$1.565594$	$-27818127/361$	$1.00533$	$3.54296$	$1$	$[0, 0, 0, -54540, 4957200]$	$y^2=x^3-54540x+4957200$	2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.?	$[ ]$	$1$
273600.ms2	273600ms1	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^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$1$	$1$		$1$	$1310720$	$1.821007$	$-27818127/361$	$1.00533$	$3.78778$	$1$	$[0, 0, 0, -151500, 22950000]$	$y^2=x^3-151500x+22950000$	2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 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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