Cremona's table of elliptic curves

48672 = 2⁵ · 3² · 13²

Field	Data	Notes
Atkin-Lehner	2+ 3+ 13-	Signs for the Atkin-Lehner involutions
Class	48672i	Isogeny class
Conductor	48672	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	-3796416 = -1 · 26 · 33 · 133	Discriminant
Eigenvalues	2+ 3+ -2  0  0 13- -8  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,39,0]	[a1,a2,a3,a4,a6]
Generators	[3:12:1] [27:144:1]	Generators of the group modulo torsion
j	1728	j-invariant
L	8.6593044012174	L(r)(E,1)/r!
Ω	1.4838536397546	Real period
R	2.9178431649936	Regulator
r	2	Rank of the group of rational points
S	0.99999999999994	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	48672i1 97344ee2 48672bi1 48672bj1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 48672i1

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	-	-8	0	0	-4	0	-12	-10	0	0	4	0	-10	0	0	-16	0	0	10	-8

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Quadratic twists for elliptic curve 48672i1

-4	8	-3	13
48672i1	97344ee2	48672bi1	48672bj1

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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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