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	16	Product of Tamagawa factors cp
Δ	144934140122954 = 2 · 74 · 138 · 37	Discriminant
Eigenvalues	2-  0 -2 7+  4 13- -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-29551,1874861]	[a1,a2,a3,a4,a6]
j	2853819360135388737/144934140122954	j-invariant
L	2.290287879897	L(r)(E,1)/r!
Ω	0.57257196997426	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	53872e3 60606m3 47138l3 87542a3	Quadratic twists by: -4 -3 -7 13

Hecke Eigenvalues for elliptic curve 6734c3

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 6734c3

-4	-3	-7	13
53872e3	60606m3	47138l3	87542a3

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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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