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	825c	Isogeny class
Conductor	825	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-2076048046875 = -1 · 3 · 58 · 116	Discriminant
Eigenvalues	0 3- 5- -1 11+ -1 -6 -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,3167,11119]	[a1,a2,a3,a4,a6]
Generators	[362:3989:8]	Generators of the group modulo torsion
j	8990228480/5314683	j-invariant
L	2.2662910334983	L(r)(E,1)/r!
Ω	0.50308198258933	Real period
R	2.2524072734963	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13200by2 52800bs2 2475k2 825a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 825c2

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
0	-	-	-1	+	-1	-6	-7	6	-6	-7	2	-6	-1	0	-6	0	5	5	-12	14	-4	-6	6	17

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Quadratic twists for elliptic curve 825c2

-4	8	-3	5	-7	-11
13200by2	52800bs2	2475k2	825a2	40425bd2	9075t2

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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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