Cremona's table of elliptic curves

24240 = 2⁴ · 3 · 5 · 101

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 101-	Signs for the Atkin-Lehner involutions
Class	24240k	Isogeny class
Conductor	24240	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	6528	Modular degree for the optimal curve
Δ	-9696000 = -1 · 28 · 3 · 53 · 101	Discriminant
Eigenvalues	2+ 3- 5+  3 -3 -4  7 -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-196,1004]	[a1,a2,a3,a4,a6]
Generators	[10:12:1]	Generators of the group modulo torsion
j	-3269383504/37875	j-invariant
L	6.4523288993454	L(r)(E,1)/r!
Ω	2.3072736676023	Real period
R	1.3982582538747	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	12120c1 96960cn1 72720s1 121200n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 24240k1

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
+	-	+	3	-3	-4	7	-1	-5	6	-7	-2	-7	8	3	10	-8	0	7	-8	-11	-1	-4	-13	-10

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Quadratic twists for elliptic curve 24240k1

-4	8	-3	5
12120c1	96960cn1	72720s1	121200n1

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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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