Cremona's table of elliptic curves

36822 = 2 · 3 · 17 · 19²

Field	Data	Notes
Atkin-Lehner	2- 3- 17- 19+	Signs for the Atkin-Lehner involutions
Class	36822bd	Isogeny class
Conductor	36822	Conductor
∏ cp	140	Product of Tamagawa factors cp
deg	112000	Modular degree for the optimal curve
Δ	261131019264 = 210 · 37 · 17 · 193	Discriminant
Eigenvalues	2- 3- -2 -4 -4 -2 17- 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-14514,671364]	[a1,a2,a3,a4,a6]
Generators	[-132:606:1] [84:-258:1]	Generators of the group modulo torsion
j	49297640752963/38071296	j-invariant
L	12.092014075394	L(r)(E,1)/r!
Ω	0.97429486469465	Real period
R	0.35460118795571	Regulator
r	2	Rank of the group of rational points
S	0.99999999999985	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	110466f1 36822f1	Quadratic twists by: -3 -19

Hecke Eigenvalues for elliptic curve 36822bd1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	-	-2	-4	-4	-2	-	+	-8	-10	-4	-10	0	0	-4	-6	-12	-8	8	2	14	8	6	-14	10

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Quadratic twists for elliptic curve 36822bd1

-3	-19
110466f1	36822f1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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