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	3621a	Isogeny class
Conductor	3621	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2640	Modular degree for the optimal curve
Δ	-15180966459 = -1 · 311 · 17 · 712	Discriminant
Eigenvalues	0 3+  3  0 -1  5 17+ -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-229,6153]	[a1,a2,a3,a4,a6]
Generators	[-21:35:1]	Generators of the group modulo torsion
j	-1333906112512/15180966459	j-invariant
L	3.0349909083431	L(r)(E,1)/r!
Ω	1.0587882474979	Real period
R	1.4332379092398	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	57936u1 10863f1 90525l1 61557c1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 3621a1

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	+	3	0	-1	5	+	-5	-9	-10	-4	6	3	5	2	-4	12	12	-4	+	-4	-10	-12	-18	2

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Quadratic twists for elliptic curve 3621a1

-4	-3	5	17
57936u1	10863f1	90525l1	61557c1

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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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