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	8976u	Isogeny class
Conductor	8976	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-1082594154774528 = -1 · 219 · 310 · 112 · 172	Discriminant
Eigenvalues	2- 3+ -2  4 11- -4 17+  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-4224,-1585152]	[a1,a2,a3,a4,a6]
Generators	[197:2278:1]	Generators of the group modulo torsion
j	-2035346265217/264305213568	j-invariant
L	3.6706029670991	L(r)(E,1)/r!
Ω	0.21778791133044	Real period
R	4.213506324428	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	1122i2 35904ck2 26928bj2 98736cr2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 8976u2

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

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Quadratic twists for elliptic curve 8976u2

-4	8	-3	-11
1122i2	35904ck2	26928bj2	98736cr2

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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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