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	1218c	Isogeny class
Conductor	1218	Conductor
∏ cp	40	Product of Tamagawa factors cp
Δ	5561943408 = 24 · 310 · 7 · 292	Discriminant
Eigenvalues	2+ 3-  0 7+  0 -6 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-451,782]	[a1,a2,a3,a4,a6]
Generators	[67:-556:1]	Generators of the group modulo torsion
j	10112728515625/5561943408	j-invariant
L	2.2316612598484	L(r)(E,1)/r!
Ω	1.1763423828539	Real period
R	0.18971188085856	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	9744i2 38976a2 3654r2 30450cg2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1218c2

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

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Quadratic twists for elliptic curve 1218c2

-4	8	-3	5	-7	29
9744i2	38976a2	3654r2	30450cg2	8526f2	35322u2

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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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