Cremona's table of elliptic curves

825 = 3 · 5² · 11

Field	Data	Notes
Atkin-Lehner	3- 5+ 11-	Signs for the Atkin-Lehner involutions
Class	825b	Isogeny class
Conductor	825	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	-91341421875 = -1 · 312 · 56 · 11	Discriminant
Eigenvalues	-1 3- 5+ -4 11-  2  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,1087,4692]	[a1,a2,a3,a4,a6]
Generators	[7:109:1]	Generators of the group modulo torsion
j	9090072503/5845851	j-invariant
L	1.7134165817794	L(r)(E,1)/r!
Ω	0.66844045463981	Real period
R	0.21360872783384	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	13200bm4 52800v3 2475g4 33a4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 825b4

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

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Quadratic twists for elliptic curve 825b4

-4	8	-3	5	-7	-11
13200bm4	52800v3	2475g4	33a4	40425y3	9075k4

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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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