Cremona's table of elliptic curves

64416 = 2⁵ · 3 · 11 · 61

Field	Data	Notes
Atkin-Lehner	2- 3+ 11+ 61-	Signs for the Atkin-Lehner involutions
Class	64416d	Isogeny class
Conductor	64416	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	204800	Modular degree for the optimal curve
Δ	205884158584896 = 26 · 310 · 114 · 612	Discriminant
Eigenvalues	2- 3+  2  0 11+  6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-14762,0]	[a1,a2,a3,a4,a6]
Generators	[-109005000:-1684954700:2146689]	Generators of the group modulo torsion
j	5559154710265792/3216939977889	j-invariant
L	6.8157332751919	L(r)(E,1)/r!
Ω	0.47530947353414	Real period
R	14.339569595949	Regulator
r	1	Rank of the group of rational points
S	0.99999999997579	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	64416c1 128832t2	Quadratic twists by: -4 8

Hecke Eigenvalues for elliptic curve 64416d1

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	+	6	-2	-4	8	6	0	6	2	-8	0	-2	-4	-	16	0	-6	0	-12	6	-14

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Quadratic twists for elliptic curve 64416d1

-4	8
64416c1	128832t2

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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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