Cremona's table of elliptic curves

49440 = 2⁵ · 3 · 5 · 103

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5- 103-	Signs for the Atkin-Lehner involutions
Class	49440c	Isogeny class
Conductor	49440	Conductor
∏ cp	84	Product of Tamagawa factors cp
deg	268800	Modular degree for the optimal curve
Δ	-1049017920000000 = -1 · 212 · 3 · 57 · 1033	Discriminant
Eigenvalues	2+ 3+ 5- -3 -6  2  3  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-17185,-1777583]	[a1,a2,a3,a4,a6]
Generators	[1389:51500:1]	Generators of the group modulo torsion
j	-137036937687616/256107890625	j-invariant
L	3.8852255783175	L(r)(E,1)/r!
Ω	0.19639382892561	Real period
R	0.23550987171644	Regulator
r	1	Rank of the group of rational points
S	0.99999999999977	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	49440o1 98880w1	Quadratic twists by: -4 8

Hecke Eigenvalues for elliptic curve 49440c1

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
+	+	-	-3	-6	2	3	2	-4	-2	-5	7	-10	-4	-7	-2	-4	13	6	8	13	12	-16	13	14

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Quadratic twists for elliptic curve 49440c1

-4	8
49440o1	98880w1

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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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