Cremona's table of elliptic curves

48400 = 2⁴ · 5² · 11²

Field	Data	Notes
Atkin-Lehner	2- 5+ 11-	Signs for the Atkin-Lehner involutions
Class	48400bw	Isogeny class
Conductor	48400	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	331776	Modular degree for the optimal curve
Δ	-29984768000000000 = -1 · 220 · 59 · 114	Discriminant
Eigenvalues	2-  1 5+ -1 11-  4  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-243008,-46936012]	[a1,a2,a3,a4,a6]
Generators	[759164:34747250:343]	Generators of the group modulo torsion
j	-1693700041/32000	j-invariant
L	7.0500299399127	L(r)(E,1)/r!
Ω	0.1073934340773	Real period
R	8.2058437749102	Regulator
r	1	Rank of the group of rational points
S	0.99999999999961	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6050bb1 9680ba1 48400bu1	Quadratic twists by: -4 5 -11

Hecke Eigenvalues for elliptic curve 48400bw1

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	-	4	0	4	0	-6	10	-8	-3	-1	9	12	-6	11	-1	6	-8	-14	-12	-15	-8

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Quadratic twists for elliptic curve 48400bw1

-4	5	-11
6050bb1	9680ba1	48400bu1

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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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