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	3648bg	Isogeny class
Conductor	3648	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	8404992 = 214 · 33 · 19	Discriminant
Eigenvalues	2- 3- -2  0  0 -2  2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-689,6735]	[a1,a2,a3,a4,a6]
Generators	[7:48:1]	Generators of the group modulo torsion
j	2211014608/513	j-invariant
L	3.7312687963579	L(r)(E,1)/r!
Ω	2.265352063309	Real period
R	0.5490344240956	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	3648i1 912b1 10944bx1 91200ey1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3648bg1

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
-	-	-2	0	0	-2	2	+	0	-2	4	-2	6	-4	0	-10	-4	2	-12	0	-6	4	-8	6	-14

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Quadratic twists for elliptic curve 3648bg1

-4	8	-3	5	-19
3648i1	912b1	10944bx1	91200ey1	69312cq1

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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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