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	3864b	Isogeny class
Conductor	3864	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	2400	Modular degree for the optimal curve
Δ	-3926071296 = -1 · 211 · 35 · 73 · 23	Discriminant
Eigenvalues	2+ 3+ -3 7+  0 -1 -4  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-392,-4116]	[a1,a2,a3,a4,a6]
j	-3261064466/1917027	j-invariant
L	0.52226108485346	L(r)(E,1)/r!
Ω	0.52226108485346	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	7728f1 30912x1 11592n1 96600ca1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3864b1

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	-4	0	-	5	-10	-3	-11	-9	-3	12	10	-10	-12	6	-4	12	12	6	9

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Quadratic twists for elliptic curve 3864b1

-4	8	-3	5	-7	-23
7728f1	30912x1	11592n1	96600ca1	27048l1	88872h1

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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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