Cremona's table of elliptic curves

3864 = 2³ · 3 · 7 · 23

Field	Data	Notes
Atkin-Lehner	2+ 3- 7+ 23-	Signs for the Atkin-Lehner involutions
Class	3864c	Isogeny class
Conductor	3864	Conductor
∏ cp	28	Product of Tamagawa factors cp
deg	1120	Modular degree for the optimal curve
Δ	-90139392 = -1 · 28 · 37 · 7 · 23	Discriminant
Eigenvalues	2+ 3-  0 7+  1 -6  0  7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,7,459]	[a1,a2,a3,a4,a6]
Generators	[-5:18:1]	Generators of the group modulo torsion
j	128000/352107	j-invariant
L	4.1018214210239	L(r)(E,1)/r!
Ω	1.4983314328005	Real period
R	0.0977711733015	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	7728d1 30912c1 11592j1 96600bo1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3864c1

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	+	1	-6	0	7	-	-10	-10	6	-5	4	-1	-3	-3	9	-4	-12	-4	-2	2	18	-6

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Quadratic twists for elliptic curve 3864c1

-4	8	-3	5	-7	-23
7728d1	30912c1	11592j1	96600bo1	27048c1	88872o1

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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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