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	48672be	Isogeny class
Conductor	48672	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	6939483992064 = 212 · 33 · 137	Discriminant
Eigenvalues	2- 3+ -2  0 -2 13+  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-34476,-2460640]	[a1,a2,a3,a4,a6]
Generators	[-107:57:1] [221:845:1]	Generators of the group modulo torsion
j	8489664/13	j-invariant
L	8.6325003467985	L(r)(E,1)/r!
Ω	0.35039691739881	Real period
R	6.159086965492	Regulator
r	2	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	48672d2 97344f1 48672a2 3744a2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 48672be2

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	-2	+	0	-4	4	-8	-8	-2	-6	-4	-6	-4	-6	2	-4	-6	2	-16	-2	-10	2

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Quadratic twists for elliptic curve 48672be2

-4	8	-3	13
48672d2	97344f1	48672a2	3744a2

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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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