Cremona's table of elliptic curves

41616 = 2⁴ · 3² · 17²

Field	Data	Notes
Atkin-Lehner	2+ 3- 17-	Signs for the Atkin-Lehner involutions
Class	41616bi	Isogeny class
Conductor	41616	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	2115072	Modular degree for the optimal curve
Δ	-1.0249676265008E+20	Discriminant
Eigenvalues	2+ 3- -4  5  0 -1 17-  3	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,103173,-486927430]	[a1,a2,a3,a4,a6]
Generators	[14161:1685448:1]	Generators of the group modulo torsion
j	23324/19683	j-invariant
L	5.0897933321608	L(r)(E,1)/r!
Ω	0.088062208532389	Real period
R	1.2041188025353	Regulator
r	1	Rank of the group of rational points
S	1.0000000000004	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	20808t1 13872g1 41616bb1	Quadratic twists by: -4 -3 17

Hecke Eigenvalues for elliptic curve 41616bi1

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
+	-	-4	5	0	-1	-	3	-6	-8	7	-3	-12	-7	6	4	10	5	-13	8	10	-8	2	4	17

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Quadratic twists for elliptic curve 41616bi1

-4	-3	17
20808t1	13872g1	41616bb1

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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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