Cremona's table of elliptic curves

8520 = 2³ · 3 · 5 · 71

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 71+	Signs for the Atkin-Lehner involutions
Class	8520b	Isogeny class
Conductor	8520	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-2981318400 = -1 · 28 · 38 · 52 · 71	Discriminant
Eigenvalues	2+ 3+ 5+ -2  0  0  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,244,2100]	[a1,a2,a3,a4,a6]
Generators	[-2:40:1]	Generators of the group modulo torsion
j	6249886256/11645775	j-invariant
L	3.0204646104883	L(r)(E,1)/r!
Ω	0.98103223806374	Real period
R	1.5394318827125	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	17040g2 68160bh2 25560m2 42600z2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8520b2

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	0	0	0	-4	2	2	8	-6	-2	8	-6	0	8	-6	14	+	10	-8	12	-14	-4

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Quadratic twists for elliptic curve 8520b2

-4	8	-3	5
17040g2	68160bh2	25560m2	42600z2

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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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