Cremona's table of elliptic curves

1005 = 3 · 5 · 67

Field	Data	Notes
Atkin-Lehner	3+ 5- 67+	Signs for the Atkin-Lehner involutions
Class	1005a	Isogeny class
Conductor	1005	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	360	Modular degree for the optimal curve
Δ	254390625 = 35 · 56 · 67	Discriminant
Eigenvalues	1 3+ 5-  0  0  4 -4  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-297,-1944]	[a1,a2,a3,a4,a6]
j	2912566550041/254390625	j-invariant
L	1.7339032275126	L(r)(E,1)/r!
Ω	1.1559354850084	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	16080y1 64320ba1 3015a1 5025e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1005a1

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	+	-	0	0	4	-4	4	8	-2	2	6	6	0	12	-2	-6	14	+	14	2	-10	-16	-18	-8

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Quadratic twists for elliptic curve 1005a1

-4	8	-3	5	-7	-11	-67
16080y1	64320ba1	3015a1	5025e1	49245t1	121605g1	67335h1

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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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