Cremona's table of elliptic curves

36064 = 2⁵ · 7² · 23

Field	Data	Notes
Atkin-Lehner	2- 7- 23+	Signs for the Atkin-Lehner involutions
Class	36064c	Isogeny class
Conductor	36064	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	18432	Modular degree for the optimal curve
Δ	-27881871808 = -1 · 26 · 77 · 232	Discriminant
Eigenvalues	2-  2  0 7-  4 -2  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,82,-8056]	[a1,a2,a3,a4,a6]
Generators	[21420:100108:729]	Generators of the group modulo torsion
j	8000/3703	j-invariant
L	8.6598494064614	L(r)(E,1)/r!
Ω	0.55401591267047	Real period
R	7.815524074678	Regulator
r	1	Rank of the group of rational points
S	0.99999999999998	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	36064e1 72128bm2 5152e1	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 36064c1

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

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Quadratic twists for elliptic curve 36064c1

-4	8	-7
36064e1	72128bm2	5152e1

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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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