Cremona's table of elliptic curves

11725 = 5² · 7 · 67

Field	Data	Notes
Atkin-Lehner	5- 7- 67+	Signs for the Atkin-Lehner involutions
Class	11725f	Isogeny class
Conductor	11725	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-27495125 = -1 · 53 · 72 · 672	Discriminant
Eigenvalues	1  0 5- 7-  2  0  2 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-22,261]	[a1,a2,a3,a4,a6]
Generators	[4:13:1]	Generators of the group modulo torsion
j	-9663597/219961	j-invariant
L	5.3619122558528	L(r)(E,1)/r!
Ω	1.7680167523407	Real period
R	1.5163635324026	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	105525bp2 11725e2 82075j2	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 11725f2

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	-	-	2	0	2	-2	4	-2	0	-4	6	-12	-8	14	10	-2	+	0	10	-10	-4	14	-16

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Quadratic twists for elliptic curve 11725f2

-3	5	-7
105525bp2	11725e2	82075j2

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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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