Cremona's table of elliptic curves

4080 = 2⁴ · 3 · 5 · 17

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 17-	Signs for the Atkin-Lehner involutions
Class	4080t	Isogeny class
Conductor	4080	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	10263060480 = 213 · 3 · 5 · 174	Discriminant
Eigenvalues	2- 3+ 5+  0 -4  2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2656,-51584]	[a1,a2,a3,a4,a6]
Generators	[-30:14:1]	Generators of the group modulo torsion
j	506071034209/2505630	j-invariant
L	2.8397960396663	L(r)(E,1)/r!
Ω	0.66520933198463	Real period
R	2.1345130796601	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	510f4 16320cz3 12240bw4 20400cy3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4080t3

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
-	+	+	0	-4	2	-	4	-4	2	4	-6	-10	8	0	6	8	10	8	-8	-2	-4	-4	-14	-10

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Quadratic twists for elliptic curve 4080t3

-4	8	-3	5	17
510f4	16320cz3	12240bw4	20400cy3	69360do3

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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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