Cremona's table of elliptic curves

7225 = 5² · 17²

Field	Data	Notes
Atkin-Lehner	5+ 17+	Signs for the Atkin-Lehner involutions
Class	7225b	Isogeny class
Conductor	7225	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	6411541765625 = 56 · 177	Discriminant
Eigenvalues	1  0 5+  4  0  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-655217,-203975184]	[a1,a2,a3,a4,a6]
Generators	[-1884000728135615376210:917714583723572604207:4033422215926741000]	Generators of the group modulo torsion
j	82483294977/17	j-invariant
L	5.3054816861484	L(r)(E,1)/r!
Ω	0.16780435960991	Real period
R	31.617067032596	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	115600bg4 65025bo4 289a3 425a3	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 7225b3

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	0	+	4	0	2	+	-4	4	-6	-4	-2	6	-4	0	-6	-12	10	-4	4	-6	-12	4	10	2

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Quadratic twists for elliptic curve 7225b3

-4	-3	5	17
115600bg4	65025bo4	289a3	425a3

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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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