Cremona's table of elliptic curves

3723 = 3 · 17 · 73

Field	Data	Notes
Atkin-Lehner	3- 17+ 73-	Signs for the Atkin-Lehner involutions
Class	3723c	Isogeny class
Conductor	3723	Conductor
∏ cp	9	Product of Tamagawa factors cp
deg	864	Modular degree for the optimal curve
Δ	-24426603 = -1 · 39 · 17 · 73	Discriminant
Eigenvalues	0 3-  0 -1  6 -4 17+ -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-193,997]	[a1,a2,a3,a4,a6]
Generators	[-1:34:1]	Generators of the group modulo torsion
j	-799178752000/24426603	j-invariant
L	3.5047656304186	L(r)(E,1)/r!
Ω	2.119068206555	Real period
R	1.6539182738796	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	59568p1 11169e1 93075d1 63291a1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 3723c1

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	-1	6	-4	+	-7	0	0	5	2	9	-10	-3	6	3	-10	-4	-3	-	-10	12	6	-10

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Quadratic twists for elliptic curve 3723c1

-4	-3	5	17
59568p1	11169e1	93075d1	63291a1

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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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