Cremona's table of elliptic curves

8904 = 2³ · 3 · 7 · 53

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 53-	Signs for the Atkin-Lehner involutions
Class	8904i	Isogeny class
Conductor	8904	Conductor
∏ cp	64	Product of Tamagawa factors cp
deg	23040	Modular degree for the optimal curve
Δ	-56120635807488 = -1 · 28 · 34 · 73 · 534	Discriminant
Eigenvalues	2- 3- -2 7+  4 -6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,5516,325952]	[a1,a2,a3,a4,a6]
j	72489947189168/219221233623	j-invariant
L	1.7701232982132	L(r)(E,1)/r!
Ω	0.44253082455331	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	17808f1 71232c1 26712d1 62328bf1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 8904i1

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	-6	2	-4	8	6	-4	-2	6	4	-8	-	0	-2	-4	-8	-2	-8	4	2	2

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Quadratic twists for elliptic curve 8904i1

-4	8	-3	-7
17808f1	71232c1	26712d1	62328bf1

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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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