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	4674c	Isogeny class
Conductor	4674	Conductor
∏ cp	36	Product of Tamagawa factors cp
deg	51840	Modular degree for the optimal curve
Δ	734471100039168 = 218 · 35 · 193 · 412	Discriminant
Eigenvalues	2- 3+  4 -4 -4  2  4 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-41721,-3027129]	[a1,a2,a3,a4,a6]
j	8031348859045152529/734471100039168	j-invariant
L	3.0240409644843	L(r)(E,1)/r!
Ω	0.33600455160936	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	37392s1 14022d1 116850ba1 88806l1	Quadratic twists by: -4 -3 5 -19

Hecke Eigenvalues for elliptic curve 4674c1

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
-	+	4	-4	-4	2	4	+	4	-2	4	-4	+	-8	10	10	12	6	4	-12	10	10	-2	-18	4

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Quadratic twists for elliptic curve 4674c1

-4	-3	5	-19
37392s1	14022d1	116850ba1	88806l1

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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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