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	4095c	Isogeny class
Conductor	4095	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	448	Modular degree for the optimal curve
Δ	159705 = 33 · 5 · 7 · 132	Discriminant
Eigenvalues	1 3+ 5+ 7-  2 13- -8  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-15,16]	[a1,a2,a3,a4,a6]
Generators	[0:4:1]	Generators of the group modulo torsion
j	14348907/5915	j-invariant
L	4.2378126367649	L(r)(E,1)/r!
Ω	2.9307363822566	Real period
R	1.4459890225616	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	65520bv1 4095f1 20475b1 28665m1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4095c1

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	+	+	-	2	-	-8	8	0	-4	-4	4	-6	-10	6	2	0	2	-8	-6	10	-12	-6	-6	-2

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Quadratic twists for elliptic curve 4095c1

-4	-3	5	-7	13
65520bv1	4095f1	20475b1	28665m1	53235d1

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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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