Cremona's table of elliptic curves

742 = 2 · 7 · 53

Field	Data	Notes
Atkin-Lehner	2+ 7+ 53+	Signs for the Atkin-Lehner involutions
Class	742a	Isogeny class
Conductor	742	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	40	Modular degree for the optimal curve
Δ	-5194 = -1 · 2 · 72 · 53	Discriminant
Eigenvalues	2+  0 -1 7+  3  4 -3  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-5,7]	[a1,a2,a3,a4,a6]
Generators	[3:2:1]	Generators of the group modulo torsion
j	-15438249/5194	j-invariant
L	1.6214759738153	L(r)(E,1)/r!
Ω	4.0625082193272	Real period
R	0.19956586993489	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	5936n1 23744d1 6678m1 18550r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 742a1

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	-1	+	3	4	-3	0	-9	0	-5	0	-2	5	-12	+	7	-10	-8	-12	-14	11	0	-13	1

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Quadratic twists for elliptic curve 742a1

-4	8	-3	5	-7	-11	13	53
5936n1	23744d1	6678m1	18550r1	5194c1	89782bf1	125398q1	39326f1

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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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