Cremona's table of elliptic curves

35131 = 19 · 43²

Field	Data	Notes
Atkin-Lehner	19+ 43+	Signs for the Atkin-Lehner involutions
Class	35131a	Isogeny class
Conductor	35131	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	2394756	Modular degree for the optimal curve
Δ	-80169365704065259 = -1 · 193 · 438	Discriminant
Eigenvalues	1 -2  2 -3  3 -2 -3 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-172879690,874896991611]	[a1,a2,a3,a4,a6]
Generators	[124918395065:-8304421214206:9938375]	Generators of the group modulo torsion
j	-48888643731442873/6859	j-invariant
L	3.8359026814071	L(r)(E,1)/r!
Ω	0.19611106787581	Real period
R	19.559848013454	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	35131e1	Quadratic twists by: -43

Hecke Eigenvalues for elliptic curve 35131a1

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	2	-3	3	-2	-3	+	-1	0	2	0	2	+	-8	4	0	-13	6	8	2	10	-15	2	16

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Quadratic twists for elliptic curve 35131a1

-43
35131e1

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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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