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	3	Product of Tamagawa factors cp
Δ	-101712857528576 = -1 · 28 · 78 · 413	Discriminant
Eigenvalues	2-  1 -3 7+  3 -4  0 -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,11548,89396]	[a1,a2,a3,a4,a6]
j	115393712/68921	j-invariant
L	1.0958535184699	L(r)(E,1)/r!
Ω	0.36528450615663	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	32144k2 128576f2 72324f2 8036f2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 8036a2

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 8036a2

-4	8	-3	-7
32144k2	128576f2	72324f2	8036f2

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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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