Cremona's table of elliptic curves

4242 = 2 · 3 · 7 · 101

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7+ 101+	Signs for the Atkin-Lehner involutions
Class	4242a	Isogeny class
Conductor	4242	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2160	Modular degree for the optimal curve
Δ	-7601664 = -1 · 29 · 3 · 72 · 101	Discriminant
Eigenvalues	2+ 3+  3 7+  6 -6  8 -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-21,-147]	[a1,a2,a3,a4,a6]
Generators	[7:7:1]	Generators of the group modulo torsion
j	-1102302937/7601664	j-invariant
L	2.8374687931944	L(r)(E,1)/r!
Ω	0.98426417355936	Real period
R	1.4414162728962	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	33936g1 12726j1 106050cb1 29694g1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4242a1

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	+	6	-6	8	-6	-6	-6	-3	-6	3	-10	-10	4	12	-9	-15	-6	-4	5	4	-9	-19

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Quadratic twists for elliptic curve 4242a1

-4	-3	5	-7
33936g1	12726j1	106050cb1	29694g1

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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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