Cremona's table of elliptic curves

7725 = 3 · 5² · 103

Field	Data	Notes
Atkin-Lehner	3- 5- 103+	Signs for the Atkin-Lehner involutions
Class	7725m	Isogeny class
Conductor	7725	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	816	Modular degree for the optimal curve
Δ	38625 = 3 · 53 · 103	Discriminant
Eigenvalues	1 3- 5-  0 -4  4  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-31,-67]	[a1,a2,a3,a4,a6]
Generators	[1245:2483:125]	Generators of the group modulo torsion
j	25153757/309	j-invariant
L	5.8958965677913	L(r)(E,1)/r!
Ω	2.0326990329787	Real period
R	5.8010521696875	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	123600bl1 23175r1 7725e1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 7725m1

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	4	6	-4	-8	6	6	2	-2	-12	-12	0	-6	-2	4	4	-2	4	12	6	-12

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Quadratic twists for elliptic curve 7725m1

-4	-3	5
123600bl1	23175r1	7725e1

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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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