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	1005b	Isogeny class
Conductor	1005	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	-890163675 = -1 · 312 · 52 · 67	Discriminant
Eigenvalues	0 3- 5+  2 -6  2 -3 -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,239,295]	[a1,a2,a3,a4,a6]
Generators	[-1:7:1]	Generators of the group modulo torsion
j	1503484706816/890163675	j-invariant
L	2.400311923811	L(r)(E,1)/r!
Ω	0.96069123660188	Real period
R	0.9369472075263	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	16080n1 64320i1 3015c1 5025a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1005b1

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	-	+	2	-6	2	-3	-1	-9	3	-4	-7	6	-10	9	-12	-15	8	-	-12	11	-4	-12	15	2

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Quadratic twists for elliptic curve 1005b1

-4	8	-3	5	-7	-11	-67
16080n1	64320i1	3015c1	5025a1	49245q1	121605k1	67335e1

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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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