Cremona's table of elliptic curves

3648 = 2⁶ · 3 · 19

Field	Data	Notes
Atkin-Lehner	2- 3+ 19-	Signs for the Atkin-Lehner involutions
Class	3648ba	Isogeny class
Conductor	3648	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-1011400704 = -1 · 214 · 32 · 193	Discriminant
Eigenvalues	2- 3+ -1  3 -5  2 -1 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,219,-963]	[a1,a2,a3,a4,a6]
Generators	[12:57:1]	Generators of the group modulo torsion
j	70575104/61731	j-invariant
L	3.0062692061588	L(r)(E,1)/r!
Ω	0.85860217295259	Real period
R	0.58355881626776	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	3648k1 912c1 10944ck1 91200ii1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3648ba1

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	-5	2	-1	-	-4	6	10	0	0	-11	-9	-10	4	5	-4	-8	13	-4	-4	-6	2

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Quadratic twists for elliptic curve 3648ba1

-4	8	-3	5	-19
3648k1	912c1	10944ck1	91200ii1	69312dk1

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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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