Cremona's table of elliptic curves

6734 = 2 · 7 · 13 · 37

Field	Data	Notes
Atkin-Lehner	2- 7+ 13- 37-	Signs for the Atkin-Lehner involutions
Class	6734c	Isogeny class
Conductor	6734	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	87542 = 2 · 7 · 132 · 37	Discriminant
Eigenvalues	2-  0 -2 7+  4 13- -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-466891,122908965]	[a1,a2,a3,a4,a6]
j	11255618047218342027777/87542	j-invariant
L	2.290287879897	L(r)(E,1)/r!
Ω	1.1451439399485	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	53872e4 60606m4 47138l4 87542a4	Quadratic twists by: -4 -3 -7 13

Hecke Eigenvalues for elliptic curve 6734c4

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	-2	+	4	-	-2	4	0	-2	-4	-	2	4	0	-10	4	14	-4	16	10	0	-16	-10	14

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Quadratic twists for elliptic curve 6734c4

-4	-3	-7	13
53872e4	60606m4	47138l4	87542a4

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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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