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	742d	Isogeny class
Conductor	742	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	-257046368945408 = -1 · 28 · 74 · 535	Discriminant
Eigenvalues	2+  3  0 7-  0  1  1 -3	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,3668,-767536]	[a1,a2,a3,a4,a6]
j	5456888637366375/257046368945408	j-invariant
L	2.1199180627627	L(r)(E,1)/r!
Ω	0.26498975784534	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	5936k1 23744t1 6678s1 18550n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 742d1

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	0	-	0	1	1	-3	5	9	-4	-3	6	-2	-2	+	-6	-12	-4	-5	-8	13	9	-6	5

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Quadratic twists for elliptic curve 742d1

-4	8	-3	5	-7	-11	13	53
5936k1	23744t1	6678s1	18550n1	5194h1	89782y1	125398l1	39326n1

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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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