Cremona's table of elliptic curves

7225 = 5² · 17²

Field	Data	Notes
Atkin-Lehner	5+ 17-	Signs for the Atkin-Lehner involutions
Class	7225f	Isogeny class
Conductor	7225	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	44064	Modular degree for the optimal curve
Δ	13624526251953125 = 59 · 178	Discriminant
Eigenvalues	0  2 5+ -2 -3 -2 17- -7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-81883,-7029457]	[a1,a2,a3,a4,a6]
j	557056/125	j-invariant
L	1.1470398988666	L(r)(E,1)/r!
Ω	0.28675997471665	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	115600ck1 65025bw1 1445e1 7225a1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 7225f1

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 7225f1

-4	-3	5	17
115600ck1	65025bw1	1445e1	7225a1

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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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