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	7242b	Isogeny class
Conductor	7242	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	23520	Modular degree for the optimal curve
Δ	-28955538198144 = -1 · 27 · 37 · 172 · 713	Discriminant
Eigenvalues	2+ 3+ -1  1  3 -6 17+  1	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-32268,-2259504]	[a1,a2,a3,a4,a6]
Generators	[8175:103378:27]	Generators of the group modulo torsion
j	-3715873205721319369/28955538198144	j-invariant
L	2.4173762964871	L(r)(E,1)/r!
Ω	0.17802161521885	Real period
R	6.7895583733339	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	57936t1 21726ba1 123114e1	Quadratic twists by: -4 -3 17

Hecke Eigenvalues for elliptic curve 7242b1

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
+	+	-1	1	3	-6	+	1	0	-1	9	2	5	5	-2	-2	3	-7	12	+	-13	-2	0	-8	-12

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Quadratic twists for elliptic curve 7242b1

-4	-3	17
57936t1	21726ba1	123114e1

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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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