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	16	Product of Tamagawa factors cp
Δ	-1722674774205 = -1 · 34 · 5 · 74 · 116	Discriminant
Eigenvalues	-1 3- 5- 7+ 11-  6 -2  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,2115,51030]	[a1,a2,a3,a4,a6]
j	590589719/972405	j-invariant
L	2.2932587218817	L(r)(E,1)/r!
Ω	0.57331468047043	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	38115k3 63525q3 88935p3 105a4	Quadratic twists by: -3 5 -7 -11

Hecke Eigenvalues for elliptic curve 12705n4

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 12705n4

-3	5	-7	-11
38115k3	63525q3	88935p3	105a4

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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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