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	742f	Isogeny class
Conductor	742	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1120	Modular degree for the optimal curve
Δ	-59884752788 = -1 · 22 · 710 · 53	Discriminant
Eigenvalues	2-  3 -2 7+  2  1  3  1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-81,11797]	[a1,a2,a3,a4,a6]
j	-58095499617/59884752788	j-invariant
L	3.5841167557621	L(r)(E,1)/r!
Ω	0.89602918894053	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5936q1 23744k1 6678d1 18550e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 742f1

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	-2	+	2	1	3	1	1	-9	0	-5	6	-6	0	+	-10	0	-4	-13	-12	1	-11	14	7

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Quadratic twists for elliptic curve 742f1

-4	8	-3	5	-7	-11	13	53
5936q1	23744k1	6678d1	18550e1	5194q1	89782m1	125398g1	39326b1

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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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