Cremona's table of elliptic curves

2424 = 2³ · 3 · 101

Field	Data	Notes
Atkin-Lehner	2+ 3+ 101-	Signs for the Atkin-Lehner involutions
Class	2424d	Isogeny class
Conductor	2424	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	232704 = 28 · 32 · 101	Discriminant
Eigenvalues	2+ 3+ -3 -4 -2 -7 -3 -3	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-17,21]	[a1,a2,a3,a4,a6]
Generators	[-3:6:1] [-1:6:1]	Generators of the group modulo torsion
j	2249728/909	j-invariant
L	2.7798572889803	L(r)(E,1)/r!
Ω	2.8454834027288	Real period
R	0.12211709293025	Regulator
r	2	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	4848g1 19392p1 7272h1 60600bl1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2424d1

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	-4	-2	-7	-3	-3	-3	-6	5	-6	2	-4	7	-12	-6	6	-2	1	-8	-11	14	-8	-10

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Quadratic twists for elliptic curve 2424d1

-4	8	-3	5	-7
4848g1	19392p1	7272h1	60600bl1	118776j1

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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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