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	3654b	Isogeny class
Conductor	3654	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	320	Modular degree for the optimal curve
Δ	-153468 = -1 · 22 · 33 · 72 · 29	Discriminant
Eigenvalues	2+ 3+  0 7+  4  2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-12,28]	[a1,a2,a3,a4,a6]
Generators	[2:2:1]	Generators of the group modulo torsion
j	-7414875/5684	j-invariant
L	2.6744577669405	L(r)(E,1)/r!
Ω	2.9825508100421	Real period
R	0.44835074694046	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	29232v1 116928i1 3654o1 91350dj1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3654b1

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

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Quadratic twists for elliptic curve 3654b1

-4	8	-3	5	-7	29
29232v1	116928i1	3654o1	91350dj1	25578b1	105966bh1

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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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