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	4	Product of Tamagawa factors cp
deg	2048	Modular degree for the optimal curve
Δ	1023942465 = 38 · 5 · 74 · 13	Discriminant
Eigenvalues	-1 3- 5- 7+ -4 13+ -6  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-257,-304]	[a1,a2,a3,a4,a6]
Generators	[-6:34:1]	Generators of the group modulo torsion
j	2565726409/1404585	j-invariant
L	2.262548939694	L(r)(E,1)/r!
Ω	1.2742382967943	Real period
R	1.7756089621432	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	65520ef1 1365c1 20475ba1 28665bg1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4095k1

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 4095k1

-4	-3	5	-7	13
65520ef1	1365c1	20475ba1	28665bg1	53235u1

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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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