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	1378265625 = 36 · 56 · 112	Discriminant
Eigenvalues	-1 3- 5+ -4 11-  2  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-288,567]	[a1,a2,a3,a4,a6]
Generators	[-9:54:1]	Generators of the group modulo torsion
j	169112377/88209	j-invariant
L	1.7134165817794	L(r)(E,1)/r!
Ω	1.3368809092796	Real period
R	0.42721745566767	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	13200bm2 52800v2 2475g2 33a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 825b2

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 825b2

-4	8	-3	5	-7	-11
13200bm2	52800v2	2475g2	33a1	40425y2	9075k2

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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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