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
Δ	22578125 = 57 · 172	Discriminant
Eigenvalues	0 -2 5+  2  3 -2 17+ -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-21533,-1223406]	[a1,a2,a3,a4,a6]
Generators	[-29176:-134:343]	Generators of the group modulo torsion
j	244534214656/5	j-invariant
L	2.406757234822	L(r)(E,1)/r!
Ω	0.39411388831873	Real period
R	3.0533778511195	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	115600bx2 65025bf2 1445a2 7225f2	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 7225a2

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 7225a2

-4	-3	5	17
115600bx2	65025bf2	1445a2	7225f2

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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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