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	6734a	Isogeny class
Conductor	6734	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	-13791232 = -1 · 212 · 7 · 13 · 37	Discriminant
Eigenvalues	2+  0  2 7+  0 13+  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,49,109]	[a1,a2,a3,a4,a6]
Generators	[21:317:27]	Generators of the group modulo torsion
j	12862247607/13791232	j-invariant
L	3.2299601091109	L(r)(E,1)/r!
Ω	1.4791318311735	Real period
R	4.3673728616175	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	53872c1 60606bc1 47138e1 87542f1	Quadratic twists by: -4 -3 -7 13

Hecke Eigenvalues for elliptic curve 6734a1

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

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Quadratic twists for elliptic curve 6734a1

-4	-3	-7	13
53872c1	60606bc1	47138e1	87542f1

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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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