Cremona's table of elliptic curves

4095 = 3² · 5 · 7 · 13

Field	Data	Notes
Atkin-Lehner	3- 5- 7+ 13+	Signs for the Atkin-Lehner involutions
Class	4095k	Isogeny class
Conductor	4095	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	373156875 = 38 · 54 · 7 · 13	Discriminant
Eigenvalues	-1 3- 5- 7+ -4 13+ -6  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-39317,3010466]	[a1,a2,a3,a4,a6]
Generators	[96:289:1]	Generators of the group modulo torsion
j	9219915604149769/511875	j-invariant
L	2.262548939694	L(r)(E,1)/r!
Ω	1.2742382967943	Real period
R	0.44390224053581	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	65520ef4 1365c3 20475ba3 28665bg4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4095k3

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
-1	-	-	+	-4	+	-6	8	4	2	-4	10	2	8	-8	-6	-8	-10	-12	8	6	8	4	-6	-2

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Quadratic twists for elliptic curve 4095k3

-4	-3	5	-7	13
65520ef4	1365c3	20475ba3	28665bg4	53235u4

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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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