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	6734b	Isogeny class
Conductor	6734	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	2520	Modular degree for the optimal curve
Δ	-147501536 = -1 · 25 · 7 · 13 · 373	Discriminant
Eigenvalues	2+  1 -2 7+ -1 13-  7 -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,123,-240]	[a1,a2,a3,a4,a6]
j	208211532983/147501536	j-invariant
L	1.0322364989751	L(r)(E,1)/r!
Ω	1.0322364989751	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	53872d1 60606bf1 47138b1 87542g1	Quadratic twists by: -4 -3 -7 13

Hecke Eigenvalues for elliptic curve 6734b1

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
+	1	-2	+	-1	-	7	-1	8	1	-6	+	-10	1	9	-6	-3	14	-8	-8	3	-16	-4	0	-16

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Quadratic twists for elliptic curve 6734b1

-4	-3	-7	13
53872d1	60606bf1	47138b1	87542g1

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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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