Cremona's table of elliptic curves

4824 = 2³ · 3² · 67

Field	Data	Notes
Atkin-Lehner	2- 3- 67+	Signs for the Atkin-Lehner involutions
Class	4824c	Isogeny class
Conductor	4824	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-60318369792 = -1 · 211 · 38 · 672	Discriminant
Eigenvalues	2- 3-  2 -2  4  4 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-219,-11882]	[a1,a2,a3,a4,a6]
Generators	[658:5805:8]	Generators of the group modulo torsion
j	-778034/40401	j-invariant
L	4.2071405524357	L(r)(E,1)/r!
Ω	0.48683620349555	Real period
R	4.3208994341709	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	9648d2 38592bf2 1608b2 120600r2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4824c2

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

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Quadratic twists for elliptic curve 4824c2

-4	8	-3	5
9648d2	38592bf2	1608b2	120600r2

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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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