Cremona's table of elliptic curves

4674 = 2 · 3 · 19 · 41

Field	Data	Notes
Atkin-Lehner	2- 3- 19+ 41+	Signs for the Atkin-Lehner involutions
Class	4674g	Isogeny class
Conductor	4674	Conductor
∏ cp	68	Product of Tamagawa factors cp
deg	3264	Modular degree for the optimal curve
Δ	-8270512128 = -1 · 217 · 34 · 19 · 41	Discriminant
Eigenvalues	2- 3-  0 -4 -1  0  0 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-703,8345]	[a1,a2,a3,a4,a6]
Generators	[38:-211:1]	Generators of the group modulo torsion
j	-38426275968625/8270512128	j-invariant
L	5.8466245369413	L(r)(E,1)/r!
Ω	1.2525035426538	Real period
R	0.068646330867781	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	37392m1 14022b1 116850d1 88806f1	Quadratic twists by: -4 -3 5 -19

Hecke Eigenvalues for elliptic curve 4674g1

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	-4	-1	0	0	+	1	-6	4	-1	+	-4	6	-8	-13	-4	-10	-13	-11	8	-8	3	11

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Quadratic twists for elliptic curve 4674g1

-4	-3	5	-19
37392m1	14022b1	116850d1	88806f1

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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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