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	3654w	Isogeny class
Conductor	3654	Conductor
∏ cp	320	Product of Tamagawa factors cp
deg	15360	Modular degree for the optimal curve
Δ	-675295187632128 = -1 · 216 · 36 · 75 · 292	Discriminant
Eigenvalues	2- 3- -2 7- -4 -2  4  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-19121,1616865]	[a1,a2,a3,a4,a6]
Generators	[63:780:1]	Generators of the group modulo torsion
j	-1060490285861833/926330847232	j-invariant
L	4.6465034643395	L(r)(E,1)/r!
Ω	0.46673965048868	Real period
R	0.12444045249516	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	29232bf1 116928ca1 406d1 91350bn1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3654w1

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	-	-4	-2	4	2	0	-	-2	2	-8	-8	-6	-6	4	4	-4	-8	-12	-12	0	-4	4

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Quadratic twists for elliptic curve 3654w1

-4	8	-3	5	-7	29
29232bf1	116928ca1	406d1	91350bn1	25578bv1	105966x1

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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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