Cremona's table of elliptic curves

35136 = 2⁶ · 3² · 61

Field	Data	Notes
Atkin-Lehner	2+ 3- 61+	Signs for the Atkin-Lehner involutions
Class	35136s	Isogeny class
Conductor	35136	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	12288	Modular degree for the optimal curve
Δ	-728580096 = -1 · 214 · 36 · 61	Discriminant
Eigenvalues	2+ 3- -3 -3 -1 -1  2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,36,-1296]	[a1,a2,a3,a4,a6]
Generators	[10:8:1] [18:-72:1]	Generators of the group modulo torsion
j	432/61	j-invariant
L	6.8486711109911	L(r)(E,1)/r!
Ω	0.75811135082059	Real period
R	1.1292323851204	Regulator
r	2	Rank of the group of rational points
S	0.99999999999991	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	35136cf1 2196f1 3904a1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 35136s1

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
+	-	-3	-3	-1	-1	2	-2	-3	-8	0	2	3	-8	4	-10	9	+	-13	12	5	-17	12	8	-18

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Quadratic twists for elliptic curve 35136s1

-4	8	-3
35136cf1	2196f1	3904a1

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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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