Cremona's table of elliptic curves

1218 = 2 · 3 · 7 · 29

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 29+	Signs for the Atkin-Lehner involutions
Class	1218k	Isogeny class
Conductor	1218	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	-137728390128 = -1 · 24 · 3 · 76 · 293	Discriminant
Eigenvalues	2- 3-  0 7-  0  2 -6  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,1067,-11695]	[a1,a2,a3,a4,a6]
j	134335727363375/137728390128	j-invariant
L	3.3744995006746	L(r)(E,1)/r!
Ω	0.56241658344576	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	9744h3 38976j3 3654m3 30450b3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1218k3

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

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Quadratic twists for elliptic curve 1218k3

-4	8	-3	5	-7	29
9744h3	38976j3	3654m3	30450b3	8526m3	35322j3

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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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