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	40656df	Isogeny class
Conductor	40656	Conductor
∏ cp	270	Product of Tamagawa factors cp
deg	207360	Modular degree for the optimal curve
Δ	1239915812357376 = 28 · 39 · 75 · 114	Discriminant
Eigenvalues	2- 3- -1 7- 11-  2  3 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-75181,7726343]	[a1,a2,a3,a4,a6]
Generators	[-37:-3234:1]	Generators of the group modulo torsion
j	12538427613184/330812181	j-invariant
L	7.3466519946598	L(r)(E,1)/r!
Ω	0.48364017202456	Real period
R	0.056260467546639	Regulator
r	1	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	10164e1 121968fn1 40656ck1	Quadratic twists by: -4 -3 -11

Hecke Eigenvalues for elliptic curve 40656df1

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	-	-	2	3	-4	2	8	10	-6	-6	7	-13	-8	11	-2	-11	-14	-14	-4	-7	1	12

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Quadratic twists for elliptic curve 40656df1

-4	-3	-11
10164e1	121968fn1	40656ck1

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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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