Cremona's table of elliptic curves

11045 = 5 · 47²

Field	Data	Notes
Atkin-Lehner	5- 47-	Signs for the Atkin-Lehner involutions
Class	11045c	Isogeny class
Conductor	11045	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	238464	Modular degree for the optimal curve
Δ	989498282154296875 = 59 · 477	Discriminant
Eigenvalues	-1 -1 5-  1 -3 -3  6  1	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-7844205,8452723552]	[a1,a2,a3,a4,a6]
Generators	[1202:27011:1]	Generators of the group modulo torsion
j	4952031207028849/91796875	j-invariant
L	2.2333266940071	L(r)(E,1)/r!
Ω	0.25561576314322	Real period
R	0.48539144729153	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	99405f1 55225b1 235b1	Quadratic twists by: -3 5 -47

Hecke Eigenvalues for elliptic curve 11045c1

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	-	1	-3	-3	6	1	-4	-2	3	0	-4	0	-	8	-6	5	-4	0	13	-10	7	14	12

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Quadratic twists for elliptic curve 11045c1

-3	5	-47
99405f1	55225b1	235b1

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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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