Cremona's table of elliptic curves

505 = 5 · 101

Field	Data	Notes
Atkin-Lehner	5+ 101+	Signs for the Atkin-Lehner involutions
Class	505a	Isogeny class
Conductor	505	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	16	Modular degree for the optimal curve
Δ	505 = 5 · 101	Discriminant
Eigenvalues	1  0 5+  0 -2  2 -6  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-10,15]	[a1,a2,a3,a4,a6]
Generators	[6:9:1]	Generators of the group modulo torsion
j	116930169/505	j-invariant
L	2.2232482832052	L(r)(E,1)/r!
Ω	5.2536146481459	Real period
R	1.6927379962973	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	8080e1 32320i1 4545c1 2525b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 505a1

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	0	+	0	-2	2	-6	0	-6	-6	8	2	2	-6	6	6	-6	2	-4	-8	10	4	0	2	-6

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Quadratic twists for elliptic curve 505a1

-4	8	-3	5	-7	-11	13	101
8080e1	32320i1	4545c1	2525b1	24745h1	61105b1	85345c1	51005a1

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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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