Cremona's table of elliptic curves

3565 = 5 · 23 · 31

Field	Data	Notes
Atkin-Lehner	5+ 23+ 31-	Signs for the Atkin-Lehner involutions
Class	3565b	Isogeny class
Conductor	3565	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	-81995 = -1 · 5 · 232 · 31	Discriminant
Eigenvalues	-2 -1 5+ -4  0  2 -1 -7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,4,12]	[a1,a2,a3,a4,a6]
Generators	[-1:2:1] [5:11:1]	Generators of the group modulo torsion
j	5451776/81995	j-invariant
L	1.8795464635764	L(r)(E,1)/r!
Ω	2.539376016853	Real period
R	0.37008037626234	Regulator
r	2	Rank of the group of rational points
S	0.99999999999968	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	57040j1 32085h1 17825d1 81995e1	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 3565b1

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	-1	+	-4	0	2	-1	-7	+	-6	-	-1	-11	-1	-12	-13	3	-8	-4	1	11	-16	7	-16	-18

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Quadratic twists for elliptic curve 3565b1

-4	-3	5	-23	-31
57040j1	32085h1	17825d1	81995e1	110515c1

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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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