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
deg	336	Modular degree for the optimal curve
Δ	-15415792 = -1 · 24 · 73 · 532	Discriminant
Eigenvalues	2+  2  4 7+ -4  2  6  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-63,245]	[a1,a2,a3,a4,a6]
j	-28344726649/15415792	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	5936r1 23744c1 6678k1 18550q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 742b1

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 742b1

-4	8	-3	5	-7	-11	13	53
5936r1	23744c1	6678k1	18550q1	5194k1	89782bk1	125398t1	39326h1

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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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