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	8036a	Isogeny class
Conductor	8036	Conductor
∏ cp	9	Product of Tamagawa factors cp
deg	8064	Modular degree for the optimal curve
Δ	-60507351296 = -1 · 28 · 78 · 41	Discriminant
Eigenvalues	2-  1 -3 7+  3 -4  0 -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2172,40004]	[a1,a2,a3,a4,a6]
j	-768208/41	j-invariant
L	1.0958535184699	L(r)(E,1)/r!
Ω	1.0958535184699	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	32144k1 128576f1 72324f1 8036f1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 8036a1

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	-3	+	3	-4	0	-7	6	6	-10	2	+	-4	12	-6	6	-13	-4	-9	14	-1	12	-12	2

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Quadratic twists for elliptic curve 8036a1

-4	8	-3	-7
32144k1	128576f1	72324f1	8036f1

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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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