Cremona's table of elliptic curves

2745 = 3² · 5 · 61

Field	Data	Notes
Atkin-Lehner	3- 5- 61+	Signs for the Atkin-Lehner involutions
Class	2745d	Isogeny class
Conductor	2745	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	-150082875 = -1 · 39 · 53 · 61	Discriminant
Eigenvalues	-2 3- 5-  1 -4  4 -4 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-57,612]	[a1,a2,a3,a4,a6]
Generators	[17:-68:1]	Generators of the group modulo torsion
j	-28094464/205875	j-invariant
L	1.8651546896864	L(r)(E,1)/r!
Ω	1.5711174790161	Real period
R	0.098929303218754	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	43920bx1 915c1 13725e1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 2745d1

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	-4	4	-4	-1	6	-3	0	-7	-2	-5	-13	-6	15	+	-4	11	-8	0	5	-2	-8

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Quadratic twists for elliptic curve 2745d1

-4	-3	5
43920bx1	915c1	13725e1

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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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