Cremona's table of elliptic curves

1185 = 3 · 5 · 79

Field	Data	Notes
Atkin-Lehner	3+ 5+ 79+	Signs for the Atkin-Lehner involutions
Class	1185a	Isogeny class
Conductor	1185	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	360	Modular degree for the optimal curve
Δ	-21063375 = -1 · 33 · 53 · 792	Discriminant
Eigenvalues	-1 3+ 5+ -4 -2  6  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,44,-172]	[a1,a2,a3,a4,a6]
Generators	[4:7:1]	Generators of the group modulo torsion
j	9407293631/21063375	j-invariant
L	1.2686975395403	L(r)(E,1)/r!
Ω	1.1173413623786	Real period
R	2.2709219979817	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	18960t1 75840bi1 3555f1 5925e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1185a1

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

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Quadratic twists for elliptic curve 1185a1

-4	8	-3	5	-7	-79
18960t1	75840bi1	3555f1	5925e1	58065s1	93615l1

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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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