Cremona's table of elliptic curves

605 = 5 · 11²

Field	Data	Notes
Atkin-Lehner	5- 11-	Signs for the Atkin-Lehner involutions
Class	605a	Isogeny class
Conductor	605	Conductor
∏ cp	15	Product of Tamagawa factors cp
deg	1320	Modular degree for the optimal curve
Δ	-669871503125 = -1 · 55 · 118	Discriminant
Eigenvalues	1 -3 5-  3 11- -4  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-1414,-44027]	[a1,a2,a3,a4,a6]
Generators	[212:2919:1]	Generators of the group modulo torsion
j	-1459161/3125	j-invariant
L	1.867102809968	L(r)(E,1)/r!
Ω	0.36480790868964	Real period
R	0.34120291172314	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	9680bf1 38720s1 5445h1 3025f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 605a1

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	-3	-	3	-	-4	0	-4	-8	-6	-2	-8	5	-5	-3	4	-2	11	-13	2	8	-10	-4	1	-8

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Quadratic twists for elliptic curve 605a1

-4	8	-3	5	-7	-11	13
9680bf1	38720s1	5445h1	3025f1	29645f1	605c1	102245f1

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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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