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	2035c	Isogeny class
Conductor	2035	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	528	Modular degree for the optimal curve
Δ	559625 = 53 · 112 · 37	Discriminant
Eigenvalues	-1 -2 5- -4 11+ -6 -6  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-100,375]	[a1,a2,a3,a4,a6]
Generators	[-10:25:1] [-5:30:1]	Generators of the group modulo torsion
j	110661134401/559625	j-invariant
L	1.8443540795037	L(r)(E,1)/r!
Ω	2.9299925951872	Real period
R	0.41964931527639	Regulator
r	2	Rank of the group of rational points
S	1.0000000000005	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	32560s1 18315l1 10175e1 99715b1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2035c1

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	-	-4	+	-6	-6	0	-4	4	-10	+	-10	-4	-2	-14	-6	0	-14	-12	16	8	-8	2	-2

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Quadratic twists for elliptic curve 2035c1

-4	-3	5	-7	-11	37
32560s1	18315l1	10175e1	99715b1	22385k1	75295a1

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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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