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	1218a	Isogeny class
Conductor	1218	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	3080	Modular degree for the optimal curve
Δ	-11051773342848 = -1 · 27 · 311 · 75 · 29	Discriminant
Eigenvalues	2+ 3+ -2 7+  1 -5  2 -5	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,1099,159789]	[a1,a2,a3,a4,a6]
j	146588258764583/11051773342848	j-invariant
L	0.5491542616125	L(r)(E,1)/r!
Ω	0.5491542616125	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	9744v1 38976o1 3654s1 30450ct1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1218a1

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	+	1	-5	2	-5	7	-	-8	7	0	-2	9	3	-1	4	5	0	5	8	15	0	15

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Quadratic twists for elliptic curve 1218a1

-4	8	-3	5	-7	29
9744v1	38976o1	3654s1	30450ct1	8526k1	35322ba1

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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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