Cremona's table of elliptic curves

3825 = 3² · 5² · 17

Field	Data	Notes
Atkin-Lehner	3- 5- 17+	Signs for the Atkin-Lehner involutions
Class	3825m	Isogeny class
Conductor	3825	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	12800	Modular degree for the optimal curve
Δ	-99991177734375 = -1 · 311 · 59 · 172	Discriminant
Eigenvalues	-1 3- 5- -4 -6  4 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-680,481322]	[a1,a2,a3,a4,a6]
Generators	[-30:703:1]	Generators of the group modulo torsion
j	-24389/70227	j-invariant
L	1.845219393486	L(r)(E,1)/r!
Ω	0.48060146188407	Real period
R	0.95984903284124	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	61200gw1 1275g1 3825o1 65025cg1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 3825m1

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

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Quadratic twists for elliptic curve 3825m1

-4	-3	5	17
61200gw1	1275g1	3825o1	65025cg1

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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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