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	40656x	Isogeny class
Conductor	40656	Conductor
∏ cp	198	Product of Tamagawa factors cp
deg	304128	Modular degree for the optimal curve
Δ	-152234890847900784 = -1 · 24 · 311 · 79 · 113	Discriminant
Eigenvalues	2+ 3- -1 7- 11+ -3  0  3	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,40704,-18490617]	[a1,a2,a3,a4,a6]
Generators	[1041:-33957:1]	Generators of the group modulo torsion
j	350208169805056/7148520419229	j-invariant
L	6.6726445404789	L(r)(E,1)/r!
Ω	0.15785184560886	Real period
R	0.21349275215583	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	20328n1 121968bq1 40656v1	Quadratic twists by: -4 -3 -11

Hecke Eigenvalues for elliptic curve 40656x1

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

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Quadratic twists for elliptic curve 40656x1

-4	-3	-11
20328n1	121968bq1	40656v1

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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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