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	32	Product of Tamagawa factors cp
Δ	12224619225 = 310 · 52 · 72 · 132	Discriminant
Eigenvalues	-1 3- 5- 7+ -4 13+ -6  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-2462,47324]	[a1,a2,a3,a4,a6]
Generators	[-18:301:1]	Generators of the group modulo torsion
j	2263054145689/16769025	j-invariant
L	2.262548939694	L(r)(E,1)/r!
Ω	1.2742382967943	Real period
R	0.88780448107161	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	65520ef2 1365c2 20475ba2 28665bg2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4095k2

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 4095k2

-4	-3	5	-7	13
65520ef2	1365c2	20475ba2	28665bg2	53235u2

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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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