Cremona's table of elliptic curves

8036 = 2² · 7² · 41

Field	Data	Notes
Atkin-Lehner	2- 7+ 41+	Signs for the Atkin-Lehner involutions
Class	8036b	Isogeny class
Conductor	8036	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	2448	Modular degree for the optimal curve
Δ	64577296 = 24 · 74 · 412	Discriminant
Eigenvalues	2- -1 -1 7+ -5 -2 -3 -3	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-506,4537]	[a1,a2,a3,a4,a6]
Generators	[-9:91:1] [6:41:1]	Generators of the group modulo torsion
j	373698304/1681	j-invariant
L	4.5236324874235	L(r)(E,1)/r!
Ω	1.9721129522201	Real period
R	0.12743332763219	Regulator
r	2	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	32144j1 128576c1 72324d1 8036e1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 8036b1

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
-	-1	-1	+	-5	-2	-3	-3	-1	-10	-11	7	+	8	-7	-11	-7	-1	7	-12	-5	9	0	-3	2

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Quadratic twists for elliptic curve 8036b1

-4	8	-3	-7
32144j1	128576c1	72324d1	8036e1

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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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