Cremona's table of elliptic curves

3621 = 3 · 17 · 71

Field	Data	Notes
Atkin-Lehner	3- 17- 71+	Signs for the Atkin-Lehner involutions
Class	3621b	Isogeny class
Conductor	3621	Conductor
∏ cp	38	Product of Tamagawa factors cp
deg	20672	Modular degree for the optimal curve
Δ	-99602320937499 = -1 · 319 · 17 · 712	Discriminant
Eigenvalues	-2 3-  3 -2 -5  1 17- -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-48654,4142360]	[a1,a2,a3,a4,a6]
Generators	[-135:2875:1]	Generators of the group modulo torsion
j	-12737620064548237312/99602320937499	j-invariant
L	2.4038378024433	L(r)(E,1)/r!
Ω	0.60161193142569	Real period
R	0.10514899428286	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	57936q1 10863e1 90525c1 61557b1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 3621b1

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	-	3	-2	-5	1	-	-1	-5	-2	6	-4	3	1	-2	8	0	0	-8	+	-2	-8	-18	-6	-16

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Quadratic twists for elliptic curve 3621b1

-4	-3	5	17
57936q1	10863e1	90525c1	61557b1

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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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