Cremona's table of elliptic curves

3663 = 3² · 11 · 37

Field	Data	Notes
Atkin-Lehner	3- 11+ 37-	Signs for the Atkin-Lehner involutions
Class	3663c	Isogeny class
Conductor	3663	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	640	Modular degree for the optimal curve
Δ	32934033 = 37 · 11 · 372	Discriminant
Eigenvalues	1 3-  0  0 11+  4 -2 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-117,432]	[a1,a2,a3,a4,a6]
Generators	[4:2:1]	Generators of the group modulo torsion
j	244140625/45177	j-invariant
L	4.2306995334189	L(r)(E,1)/r!
Ω	1.9734219522867	Real period
R	2.1438392982892	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	58608bm1 1221c1 91575t1 40293l1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 3663c1

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	-	0	0	+	4	-2	-2	6	-2	4	-	-6	6	-12	-2	-10	0	4	-16	2	-14	-12	-12	10

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Quadratic twists for elliptic curve 3663c1

-4	-3	5	-11
58608bm1	1221c1	91575t1	40293l1

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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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