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	4095h	Isogeny class
Conductor	4095	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	4975425 = 37 · 52 · 7 · 13	Discriminant
Eigenvalues	-1 3- 5+ 7+ -4 13-  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1283,18002]	[a1,a2,a3,a4,a6]
Generators	[-27:193:1]	Generators of the group modulo torsion
j	320153881321/6825	j-invariant
L	1.9653679309181	L(r)(E,1)/r!
Ω	2.2427032243834	Real period
R	1.7526776700099	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	65520dd1 1365f1 20475x1 28665bt1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4095h1

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	-	2	4	-4	-6	8	-2	-2	-4	12	2	0	14	-4	0	10	-8	0	6	-14

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Quadratic twists for elliptic curve 4095h1

-4	-3	5	-7	13
65520dd1	1365f1	20475x1	28665bt1	53235bj1

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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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