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	12705n	Isogeny class
Conductor	12705	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	5760	Modular degree for the optimal curve
Δ	186013905 = 3 · 5 · 7 · 116	Discriminant
Eigenvalues	-1 3- 5- 7+ 11-  6 -2  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-305,-1968]	[a1,a2,a3,a4,a6]
j	1771561/105	j-invariant
L	2.2932587218817	L(r)(E,1)/r!
Ω	1.1466293609409	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	38115k1 63525q1 88935p1 105a1	Quadratic twists by: -3 5 -7 -11

Hecke Eigenvalues for elliptic curve 12705n1

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	-	-	+	-	6	-2	8	8	2	4	-2	6	-4	8	10	4	2	4	-12	2	-8	4	-6	-18

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Quadratic twists for elliptic curve 12705n1

-3	5	-7	-11
38115k1	63525q1	88935p1	105a1

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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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