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	12	Product of Tamagawa factors cp
Δ	-33133870125 = -1 · 310 · 53 · 672	Discriminant
Eigenvalues	1 3+ 5-  0  0  4 -4  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,328,-8319]	[a1,a2,a3,a4,a6]
j	3883959939959/33133870125	j-invariant
L	1.7339032275126	L(r)(E,1)/r!
Ω	0.5779677425042	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	16080y2 64320ba2 3015a2 5025e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1005a2

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 1005a2

-4	8	-3	5	-7	-11	-67
16080y2	64320ba2	3015a2	5025e2	49245t2	121605g2	67335h2

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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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