Cremona's table of elliptic curves

12705 = 3 · 5 · 7 · 11²

Field	Data	Notes
Atkin-Lehner	3+ 5+ 7- 11-	Signs for the Atkin-Lehner involutions
Class	12705c	Isogeny class
Conductor	12705	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	701830463565 = 3 · 5 · 74 · 117	Discriminant
Eigenvalues	1 3+ 5+ 7- 11-  2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-106603,-13441292]	[a1,a2,a3,a4,a6]
Generators	[3894:54785:8]	Generators of the group modulo torsion
j	75627935783569/396165	j-invariant
L	4.1756489444574	L(r)(E,1)/r!
Ω	0.26421459501768	Real period
R	7.9020028098333	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	38115bd4 63525bi4 88935cg4 1155a3	Quadratic twists by: -3 5 -7 -11

Hecke Eigenvalues for elliptic curve 12705c3

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

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Quadratic twists for elliptic curve 12705c3

-3	5	-7	-11
38115bd4	63525bi4	88935cg4	1155a3

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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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