Cremona's table of elliptic curves

40656 = 2⁴ · 3 · 7 · 11²

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 11+	Signs for the Atkin-Lehner involutions
Class	40656cz	Isogeny class
Conductor	40656	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	36864	Modular degree for the optimal curve
Δ	3205644288 = 214 · 3 · 72 · 113	Discriminant
Eigenvalues	2- 3-  4 7- 11+ -2  6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-656,5652]	[a1,a2,a3,a4,a6]
j	5735339/588	j-invariant
L	5.5027133696805	L(r)(E,1)/r!
Ω	1.3756783424439	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	5082o1 121968fi1 40656cd1	Quadratic twists by: -4 -3 -11

Hecke Eigenvalues for elliptic curve 40656cz1

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	-	+	-2	6	-2	2	6	0	-10	2	10	-10	4	-4	-10	-12	-10	8	-4	12	2	14

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Quadratic twists for elliptic curve 40656cz1

-4	-3	-11
5082o1	121968fi1	40656cd1

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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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