Cremona's table of elliptic curves

8976 = 2⁴ · 3 · 11 · 17

Field	Data	Notes
Atkin-Lehner	2- 3+ 11+ 17-	Signs for the Atkin-Lehner involutions
Class	8976r	Isogeny class
Conductor	8976	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	1289097216 = 212 · 32 · 112 · 172	Discriminant
Eigenvalues	2- 3+  2  0 11+ -2 17- -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-272,0]	[a1,a2,a3,a4,a6]
Generators	[-8:40:1]	Generators of the group modulo torsion
j	545338513/314721	j-invariant
L	4.1102205755267	L(r)(E,1)/r!
Ω	1.2822188398034	Real period
R	1.6027765494995	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	561d2 35904de2 26928bn2 98736bv2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 8976r2

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

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Quadratic twists for elliptic curve 8976r2

-4	8	-3	-11
561d2	35904de2	26928bn2	98736bv2

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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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