Cremona's table of elliptic curves

7225 = 5² · 17²

Field	Data	Notes
Atkin-Lehner	5+ 17+	Signs for the Atkin-Lehner involutions
Class	7225a	Isogeny class
Conductor	7225	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2592	Modular degree for the optimal curve
Δ	564453125 = 59 · 172	Discriminant
Eigenvalues	0 -2 5+  2  3 -2 17+ -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-283,-1531]	[a1,a2,a3,a4,a6]
Generators	[-7:12:1]	Generators of the group modulo torsion
j	557056/125	j-invariant
L	2.406757234822	L(r)(E,1)/r!
Ω	1.1823416649562	Real period
R	1.0177926170398	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	115600bx1 65025bf1 1445a1 7225f1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 7225a1

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	-2	+	2	3	-2	+	-7	6	3	-8	-4	-9	-2	12	0	-9	7	16	3	-16	1	12	9	2

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Quadratic twists for elliptic curve 7225a1

-4	-3	5	17
115600bx1	65025bf1	1445a1	7225f1

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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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