Cremona's table of elliptic curves

387 = 3² · 43

Field	Data	Notes
Atkin-Lehner	3+ 43+	Signs for the Atkin-Lehner involutions
Class	387c	Isogeny class
Conductor	387	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	16	Modular degree for the optimal curve
Δ	-1161 = -1 · 33 · 43	Discriminant
Eigenvalues	-1 3+  1 -3  3 -5 -6  1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-2,2]	[a1,a2,a3,a4,a6]
Generators	[0:1:1]	Generators of the group modulo torsion
j	-19683/43	j-invariant
L	1.2498477541587	L(r)(E,1)/r!
Ω	4.3310513611835	Real period
R	0.14428918638096	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	6192k1 24768f1 387b1 9675a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 387c1

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
-1	+	1	-3	3	-5	-6	1	-8	9	-4	-6	-8	+	-1	8	0	-10	12	-2	2	10	15	-2	-11

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Quadratic twists for elliptic curve 387c1

-4	8	-3	5	-7	-11	13	17	-43
6192k1	24768f1	387b1	9675a1	18963b1	46827e1	65403a1	111843c1	16641c1

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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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