Cremona's table of elliptic curves

2035 = 5 · 11 · 37

Field	Data	Notes
Atkin-Lehner	5+ 11+ 37-	Signs for the Atkin-Lehner involutions
Class	2035b	Isogeny class
Conductor	2035	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	27720	Modular degree for the optimal curve
Δ	-32989161914396875 = -1 · 55 · 1111 · 37	Discriminant
Eigenvalues	-2  0 5+  1 11+ -6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-365513,85503218]	[a1,a2,a3,a4,a6]
j	-5400477932182072602624/32989161914396875	j-invariant
L	0.37101454872604	L(r)(E,1)/r!
Ω	0.37101454872604	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	32560k1 18315v1 10175d1 99715m1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2035b1

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
-2	0	+	1	+	-6	-2	-4	-3	9	4	-	-12	12	4	0	-6	-5	-2	13	2	-3	11	4	5

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Quadratic twists for elliptic curve 2035b1

-4	-3	5	-7	-11	37
32560k1	18315v1	10175d1	99715m1	22385h1	75295k1

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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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