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	742b	Isogeny class
Conductor	742	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	24941588 = 22 · 76 · 53	Discriminant
Eigenvalues	2+  2  4 7+ -4  2  6  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1123,14025]	[a1,a2,a3,a4,a6]
j	156843708284089/24941588	j-invariant
L	2.0545031091529	L(r)(E,1)/r!
Ω	2.0545031091529	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	5936r2 23744c2 6678k2 18550q2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 742b2

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
+	2	4	+	-4	2	6	2	0	6	-2	-6	-4	4	-8	-	4	8	-8	-12	-12	8	-2	14	-18

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Quadratic twists for elliptic curve 742b2

-4	8	-3	5	-7	-11	13	53
5936r2	23744c2	6678k2	18550q2	5194k2	89782bk2	125398t2	39326h2

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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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