Cremona's table of elliptic curves

3654 = 2 · 3² · 7 · 29

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7+ 29+	Signs for the Atkin-Lehner involutions
Class	3654a	Isogeny class
Conductor	3654	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	33120	Modular degree for the optimal curve
Δ	-1642378725163008 = -1 · 223 · 39 · 73 · 29	Discriminant
Eigenvalues	2+ 3+  0 7+ -1 -3  8  1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-860532,-307045936]	[a1,a2,a3,a4,a6]
Generators	[1729066075:415636629328:29791]	Generators of the group modulo torsion
j	-3580418379458257875/83441483776	j-invariant
L	2.5390535208469	L(r)(E,1)/r!
Ω	0.078374931073667	Real period
R	16.198122831268	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	29232u1 116928f1 3654n1 91350df1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3654a1

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
+	+	0	+	-1	-3	8	1	-3	+	0	-5	4	4	5	1	11	-14	-7	-8	3	-4	-9	0	-3

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Quadratic twists for elliptic curve 3654a1

-4	8	-3	5	-7	29
29232u1	116928f1	3654n1	91350df1	25578a1	105966bg1

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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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