Cremona's table of elliptic curves

7225 = 5² · 17²

Field	Data	Notes
Atkin-Lehner	5+ 17+	Signs for the Atkin-Lehner involutions
Class	7225d	Isogeny class
Conductor	7225	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1728	Modular degree for the optimal curve
Δ	-22578125 = -1 · 57 · 172	Discriminant
Eigenvalues	-1 -1 5+ -5 -2 -2 17+  6	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,62,156]	[a1,a2,a3,a4,a6]
Generators	[0:12:1]	Generators of the group modulo torsion
j	5831/5	j-invariant
L	1.2306908351478	L(r)(E,1)/r!
Ω	1.3904324939394	Real period
R	0.22127842245348	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	115600bk1 65025bm1 1445c1 7225g1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 7225d1

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	+	-5	-2	-2	+	6	-9	6	-8	2	-1	-4	0	4	2	2	7	-10	4	8	11	-3	2

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Quadratic twists for elliptic curve 7225d1

-4	-3	5	17
115600bk1	65025bm1	1445c1	7225g1

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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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