Cremona's table of elliptic curves

2775 = 3 · 5² · 37

Field	Data	Notes
Atkin-Lehner	3- 5- 37+	Signs for the Atkin-Lehner involutions
Class	2775h	Isogeny class
Conductor	2775	Conductor
∏ cp	30	Product of Tamagawa factors cp
deg	720	Modular degree for the optimal curve
Δ	-207916875 = -1 · 35 · 54 · 372	Discriminant
Eigenvalues	0 3- 5-  1 -2 -1  4 -3	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-83,-781]	[a1,a2,a3,a4,a6]
Generators	[43:277:1]	Generators of the group modulo torsion
j	-102400000/332667	j-invariant
L	3.312825606875	L(r)(E,1)/r!
Ω	0.72778563372464	Real period
R	0.15173083269592	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	44400bs1 8325ba1 2775b1 102675u1	Quadratic twists by: -4 -3 5 37

Hecke Eigenvalues for elliptic curve 2775h1

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	-2	-1	4	-3	-6	-6	-9	+	6	7	12	-12	2	13	-11	0	-6	0	-4	-14	-13

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Quadratic twists for elliptic curve 2775h1

-4	-3	5	37
44400bs1	8325ba1	2775b1	102675u1

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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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