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	742c	Isogeny class
Conductor	742	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	600	Modular degree for the optimal curve
Δ	-87140859904 = -1 · 225 · 72 · 53	Discriminant
Eigenvalues	2+  0  3 7-  3  4  1  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,727,11853]	[a1,a2,a3,a4,a6]
j	42461064302103/87140859904	j-invariant
L	1.4888999537109	L(r)(E,1)/r!
Ω	0.74444997685544	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	5936h1 23744o1 6678u1 18550m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 742c1

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	4	1	0	-1	0	-1	0	6	-11	4	+	3	6	8	4	10	-5	0	-9	5

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Quadratic twists for elliptic curve 742c1

-4	8	-3	5	-7	-11	13	53
5936h1	23744o1	6678u1	18550m1	5194d1	89782u1	125398j1	39326k1

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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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