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	3648z	Isogeny class
Conductor	3648	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	256	Modular degree for the optimal curve
Δ	-98496 = -1 · 26 · 34 · 19	Discriminant
Eigenvalues	2- 3+  1  1  3  0 -7 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,5,13]	[a1,a2,a3,a4,a6]
Generators	[4:9:1]	Generators of the group modulo torsion
j	175616/1539	j-invariant
L	3.3588478965366	L(r)(E,1)/r!
Ω	2.4661848616263	Real period
R	0.68098056005454	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	3648bd1 1824h1 10944cl1 91200ib1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3648z1

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	1	3	0	-7	-	-8	0	2	-4	-4	-1	3	-6	-6	5	-2	2	-11	10	16	-14	-8

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Quadratic twists for elliptic curve 3648z1

-4	8	-3	5	-19
3648bd1	1824h1	10944cl1	91200ib1	69312dj1

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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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