Cremona's table of elliptic curves

2475 = 3² · 5² · 11

Field	Data	Notes
Atkin-Lehner	3+ 5- 11-	Signs for the Atkin-Lehner involutions
Class	2475f	Isogeny class
Conductor	2475	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-185625 = -1 · 33 · 54 · 11	Discriminant
Eigenvalues	-1 3+ 5- -3 11-  2 -3 -1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-5,22]	[a1,a2,a3,a4,a6]
Generators	[4:-10:1]	Generators of the group modulo torsion
j	-675/11	j-invariant
L	1.9004047305698	L(r)(E,1)/r!
Ω	2.6979700159286	Real period
R	0.11739719859437	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	39600cm1 2475e1 2475c1 121275cd1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2475f1

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	+	-	-3	-	2	-3	-1	-1	6	4	1	-5	4	-3	-10	11	14	2	-5	2	5	-8	-10	-17

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Quadratic twists for elliptic curve 2475f1

-4	-3	5	-7	-11
39600cm1	2475e1	2475c1	121275cd1	27225w1

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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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