Cremona's table of elliptic curves

1085 = 5 · 7 · 31

Field	Data	Notes
Atkin-Lehner	5- 7+ 31+	Signs for the Atkin-Lehner involutions
Class	1085f	Isogeny class
Conductor	1085	Conductor
∏ cp	34	Product of Tamagawa factors cp
deg	13056	Modular degree for the optimal curve
Δ	-5132293701171875 = -1 · 517 · 7 · 312	Discriminant
Eigenvalues	2  3 5- 7+ -1 -1  1 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-33967,-4205495]	[a1,a2,a3,a4,a6]
j	-4334063657515831296/5132293701171875	j-invariant
L	5.7183505638455	L(r)(E,1)/r!
Ω	0.16818678128957	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	17360bm1 69440e1 9765c1 5425f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1085f1

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	3	-	+	-1	-1	1	-2	4	-3	+	2	0	-6	-7	2	10	-14	4	4	-2	1	-12	16	11

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Quadratic twists for elliptic curve 1085f1

-4	8	-3	5	-7	-31
17360bm1	69440e1	9765c1	5425f1	7595f1	33635n1

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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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