Cremona's table of elliptic curves

1518 = 2 · 3 · 11 · 23

Field	Data	Notes
Atkin-Lehner	2+ 3- 11+ 23-	Signs for the Atkin-Lehner involutions
Class	1518h	Isogeny class
Conductor	1518	Conductor
∏ cp	36	Product of Tamagawa factors cp
deg	2880	Modular degree for the optimal curve
Δ	2276047011744 = 25 · 312 · 11 · 233	Discriminant
Eigenvalues	2+ 3- -3 -1 11+  5 -3  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-4580,-95038]	[a1,a2,a3,a4,a6]
Generators	[-48:145:1]	Generators of the group modulo torsion
j	10621450496611513/2276047011744	j-invariant
L	2.1083353122571	L(r)(E,1)/r!
Ω	0.58917121215319	Real period
R	0.89461911443022	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	12144x1 48576w1 4554bf1 37950bt1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1518h1

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
+	-	-3	-1	+	5	-3	2	-	-3	-1	-1	0	-10	-3	-6	0	-10	-7	-3	-4	-1	-6	-12	8

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Quadratic twists for elliptic curve 1518h1

-4	8	-3	5	-7	-11	-23
12144x1	48576w1	4554bf1	37950bt1	74382d1	16698bq1	34914r1

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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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