Cremona's table of elliptic curves

4896 = 2⁵ · 3² · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 17-	Signs for the Atkin-Lehner involutions
Class	4896d	Isogeny class
Conductor	4896	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-107868672 = -1 · 29 · 36 · 172	Discriminant
Eigenvalues	2+ 3-  0  2 -4  2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,45,486]	[a1,a2,a3,a4,a6]
Generators	[-3:18:1]	Generators of the group modulo torsion
j	27000/289	j-invariant
L	3.9664710876575	L(r)(E,1)/r!
Ω	1.3839651935667	Real period
R	0.71650484891082	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	4896q2 9792s2 544d2 122400dc2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4896d2

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

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Quadratic twists for elliptic curve 4896d2

-4	8	-3	5	17
4896q2	9792s2	544d2	122400dc2	83232e2

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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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