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	1085b	Isogeny class
Conductor	1085	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	3360	Modular degree for the optimal curve
Δ	-330288932402555 = -1 · 5 · 74 · 317	Discriminant
Eigenvalues	0  1 5+ 7-  4 -2  3 -5	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,12859,674791]	[a1,a2,a3,a4,a6]
j	235131885842333696/330288932402555	j-invariant
L	1.4649880735471	L(r)(E,1)/r!
Ω	0.36624701838676	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	17360t1 69440bs1 9765m1 5425a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1085b1

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
0	1	+	-	4	-2	3	-5	8	10	+	-5	9	11	2	-9	7	8	10	-7	9	6	-9	-12	6

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Quadratic twists for elliptic curve 1085b1

-4	8	-3	5	-7	-31
17360t1	69440bs1	9765m1	5425a1	7595j1	33635c1

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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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