Cremona's table of elliptic curves

1206 = 2 · 3² · 67

Field	Data	Notes
Atkin-Lehner	2+ 3- 67+	Signs for the Atkin-Lehner involutions
Class	1206b	Isogeny class
Conductor	1206	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-4771277298 = -1 · 2 · 312 · 672	Discriminant
Eigenvalues	2+ 3- -2  2  4  0 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-243,-3569]	[a1,a2,a3,a4,a6]
j	-2181825073/6544962	j-invariant
L	1.1175346810175	L(r)(E,1)/r!
Ω	0.55876734050875	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	9648r2 38592bc2 402c2 30150cm2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1206b2

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
+	-	-2	2	4	0	-6	4	6	-8	2	-2	10	4	6	6	8	8	+	14	-6	-2	12	6	-2

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Quadratic twists for elliptic curve 1206b2

-4	8	-3	5	-7	-67
9648r2	38592bc2	402c2	30150cm2	59094v2	80802o2

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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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