Cremona's table of elliptic curves

387 = 3² · 43

Field	Data	Notes
Atkin-Lehner	3+ 43+	Signs for the Atkin-Lehner involutions
Class	387b	Isogeny class
Conductor	387	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	-846369 = -1 · 39 · 43	Discriminant
Eigenvalues	1 3+ -1 -3 -3 -5  6  1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-15,-46]	[a1,a2,a3,a4,a6]
Generators	[10:22:1]	Generators of the group modulo torsion
j	-19683/43	j-invariant
L	1.9788330814827	L(r)(E,1)/r!
Ω	1.1323623367511	Real period
R	0.87376320160924	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	6192l1 24768e1 387c1 9675d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 387b1

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 387b1

-4	8	-3	5	-7	-11	13	17	-43
6192l1	24768e1	387c1	9675d1	18963a1	46827g1	65403b1	111843a1	16641d1

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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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