Cremona's table of elliptic curves

8514 = 2 · 3² · 11 · 43

Field	Data	Notes
Atkin-Lehner	2+ 3- 11- 43+	Signs for the Atkin-Lehner involutions
Class	8514d	Isogeny class
Conductor	8514	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	31205394421531308 = 22 · 39 · 118 · 432	Discriminant
Eigenvalues	2+ 3-  2  0 11- -2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-9587961,11429532945]	[a1,a2,a3,a4,a6]
Generators	[1170:41985:1]	Generators of the group modulo torsion
j	133713416563031354522257/42805753664652	j-invariant
L	3.7223854052182	L(r)(E,1)/r!
Ω	0.29852713737144	Real period
R	1.558646157764	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	68112bu6 2838e5 93654bp6	Quadratic twists by: -4 -3 -11

Hecke Eigenvalues for elliptic curve 8514d5

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

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Quadratic twists for elliptic curve 8514d5

-4	-3	-11
68112bu6	2838e5	93654bp6

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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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