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	2775j	Isogeny class
Conductor	2775	Conductor
∏ cp	54	Product of Tamagawa factors cp
deg	10800	Modular degree for the optimal curve
Δ	-10525791796875 = -1 · 39 · 58 · 372	Discriminant
Eigenvalues	-2 3- 5-  1  0 -5 -4  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-19708,1069744]	[a1,a2,a3,a4,a6]
Generators	[158:1387:1]	Generators of the group modulo torsion
j	-2167271772160/26946027	j-invariant
L	2.0812957168274	L(r)(E,1)/r!
Ω	0.72440303600058	Real period
R	0.053205896937392	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	44400br1 8325bc1 2775d1 102675w1	Quadratic twists by: -4 -3 5 37

Hecke Eigenvalues for elliptic curve 2775j1

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
-2	-	-	1	0	-5	-4	5	4	2	-9	+	4	-13	-4	-12	12	5	1	-6	-10	0	-18	8	-1

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Quadratic twists for elliptic curve 2775j1

-4	-3	5	37
44400br1	8325bc1	2775d1	102675w1

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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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