Cremona's table of elliptic curves

5225 = 5² · 11 · 19

Field	Data	Notes
Atkin-Lehner	5+ 11- 19-	Signs for the Atkin-Lehner involutions
Class	5225c	Isogeny class
Conductor	5225	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	2592	Modular degree for the optimal curve
Δ	-7507671875 = -1 · 56 · 113 · 192	Discriminant
Eigenvalues	0 -1 5+  4 11- -2  0 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-683,8268]	[a1,a2,a3,a4,a6]
Generators	[-4:104:1]	Generators of the group modulo torsion
j	-2258403328/480491	j-invariant
L	2.8681335557414	L(r)(E,1)/r!
Ω	1.2630621572934	Real period
R	0.37846297312444	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	83600be1 47025r1 209a1 57475g1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 5225c1

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
0	-1	+	4	-	-2	0	-	-3	-6	-7	7	0	10	0	-6	3	-10	-11	15	-8	-16	0	9	1

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Quadratic twists for elliptic curve 5225c1

-4	-3	5	-11	-19
83600be1	47025r1	209a1	57475g1	99275d1

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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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