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	4	Product of Tamagawa factors cp
Δ	-255025 = -1 · 52 · 1012	Discriminant
Eigenvalues	1  0 5+  0 -2  2 -6  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-5,26]	[a1,a2,a3,a4,a6]
Generators	[-2:6:1]	Generators of the group modulo torsion
j	-15438249/255025	j-invariant
L	2.2232482832052	L(r)(E,1)/r!
Ω	2.626807324073	Real period
R	0.84636899814867	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	8080e2 32320i2 4545c2 2525b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 505a2

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 505a2

-4	8	-3	5	-7	-11	13	101
8080e2	32320i2	4545c2	2525b2	24745h2	61105b2	85345c2	51005a2

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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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