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	3654r	Isogeny class
Conductor	3654	Conductor
∏ cp	64	Product of Tamagawa factors cp
deg	2560	Modular degree for the optimal curve
Δ	-64441827072 = -1 · 28 · 311 · 72 · 29	Discriminant
Eigenvalues	2- 3-  0 7+  0 -6  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,985,-2977]	[a1,a2,a3,a4,a6]
Generators	[9:76:1]	Generators of the group modulo torsion
j	145116956375/88397568	j-invariant
L	4.9534728019878	L(r)(E,1)/r!
Ω	0.63984097559324	Real period
R	0.48385780519479	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	29232bi1 116928bf1 1218c1 91350bq1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3654r1

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

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Quadratic twists for elliptic curve 3654r1

-4	8	-3	5	-7	29
29232bi1	116928bf1	1218c1	91350bq1	25578bi1	105966k1

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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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