Cremona's table of elliptic curves

6474 = 2 · 3 · 13 · 83

Field	Data	Notes
Atkin-Lehner	2+ 3+ 13+ 83+	Signs for the Atkin-Lehner involutions
Class	6474b	Isogeny class
Conductor	6474	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	23296	Modular degree for the optimal curve
Δ	-60471089821584 = -1 · 24 · 313 · 134 · 83	Discriminant
Eigenvalues	2+ 3+  3  0  1 13+  0 -1	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-23506,1426948]	[a1,a2,a3,a4,a6]
Generators	[72:302:1]	Generators of the group modulo torsion
j	-1436444252133760297/60471089821584	j-invariant
L	3.1372523098541	L(r)(E,1)/r!
Ω	0.61863473553305	Real period
R	1.2678128666469	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	51792m1 19422r1 84162q1	Quadratic twists by: -4 -3 13

Hecke Eigenvalues for elliptic curve 6474b1

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	1	+	0	-1	-7	8	-10	7	-2	-4	0	-1	-5	-9	5	-4	-4	4	+	-15	2

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Quadratic twists for elliptic curve 6474b1

-4	-3	13
51792m1	19422r1	84162q1

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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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