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	72	Product of Tamagawa factors cp
Δ	274663872 = 26 · 36 · 7 · 292	Discriminant
Eigenvalues	2- 3-  0 7-  0  2 -6  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-2373,44289]	[a1,a2,a3,a4,a6]
j	1477843225692625/274663872	j-invariant
L	3.3744995006746	L(r)(E,1)/r!
Ω	1.6872497503373	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	9744h2 38976j2 3654m2 30450b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1218k2

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 1218k2

-4	8	-3	5	-7	29
9744h2	38976j2	3654m2	30450b2	8526m2	35322j2

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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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