Cremona's table of elliptic curves

3036 = 2² · 3 · 11 · 23

Field	Data	Notes
Atkin-Lehner	2- 3- 11- 23-	Signs for the Atkin-Lehner involutions
Class	3036j	Isogeny class
Conductor	3036	Conductor
∏ cp	30	Product of Tamagawa factors cp
deg	1440	Modular degree for the optimal curve
Δ	239030352 = 24 · 310 · 11 · 23	Discriminant
Eigenvalues	2- 3- -4  0 11- -2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-165,-396]	[a1,a2,a3,a4,a6]
Generators	[-3:9:1]	Generators of the group modulo torsion
j	31238127616/14939397	j-invariant
L	3.2200535689855	L(r)(E,1)/r!
Ω	1.395909906215	Real period
R	0.30757033383973	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	12144r1 48576n1 9108j1 75900h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3036j1

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	0	-	-2	6	-4	-	4	4	-6	0	-8	0	-12	-4	-2	2	-16	-10	-12	-4	8	-10

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Quadratic twists for elliptic curve 3036j1

-4	8	-3	5	-11	-23
12144r1	48576n1	9108j1	75900h1	33396t1	69828ba1

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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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