Cremona's table of elliptic curves

7242 = 2 · 3 · 17 · 71

Field	Data	Notes
Atkin-Lehner	2+ 3+ 17+ 71+	Signs for the Atkin-Lehner involutions
Class	7242a	Isogeny class
Conductor	7242	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	65178 = 2 · 33 · 17 · 71	Discriminant
Eigenvalues	2+ 3+  0 -3 -3 -1 17+  6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-170,786]	[a1,a2,a3,a4,a6]
Generators	[7:-3:1]	Generators of the group modulo torsion
j	548347731625/65178	j-invariant
L	2.0843172628587	L(r)(E,1)/r!
Ω	3.3528078068327	Real period
R	0.62166320974649	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	57936s1 21726z1 123114d1	Quadratic twists by: -4 -3 17

Hecke Eigenvalues for elliptic curve 7242a1

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	-3	-3	-1	+	6	-2	10	0	-7	6	4	-9	14	-2	10	7	+	-10	4	1	-4	11

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Quadratic twists for elliptic curve 7242a1

-4	-3	17
57936s1	21726z1	123114d1

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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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