Cremona's table of elliptic curves

418 = 2 · 11 · 19

Field	Data	Notes
Atkin-Lehner	2- 11+ 19-	Signs for the Atkin-Lehner involutions
Class	418b	Isogeny class
Conductor	418	Conductor
∏ cp	26	Product of Tamagawa factors cp
deg	104	Modular degree for the optimal curve
Δ	-18833408 = -1 · 213 · 112 · 19	Discriminant
Eigenvalues	2- -1 -2 -3 11+  1 -7 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,66,-5]	[a1,a2,a3,a4,a6]
Generators	[5:19:1]	Generators of the group modulo torsion
j	31764658463/18833408	j-invariant
L	1.9863516581669	L(r)(E,1)/r!
Ω	1.2722415997095	Real period
R	0.060050025652492	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3344i1 13376h1 3762j1 10450b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 418b1

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

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Quadratic twists for elliptic curve 418b1

-4	8	-3	5	-7	-11	13	17	-19
3344i1	13376h1	3762j1	10450b1	20482h1	4598f1	70642d1	120802o1	7942d1

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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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