Cremona's table of elliptic curves

415 = 5 · 83

Field	Data	Notes
Atkin-Lehner	5- 83+	Signs for the Atkin-Lehner involutions
Class	415a	Isogeny class
Conductor	415	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	112	Modular degree for the optimal curve
Δ	-51875 = -1 · 54 · 83	Discriminant
Eigenvalues	1  3 5-  1  3 -6 -7  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-109,-412]	[a1,a2,a3,a4,a6]
j	-143960212521/51875	j-invariant
L	2.9537717476034	L(r)(E,1)/r!
Ω	0.73844293690085	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	6640i1 26560e1 3735d1 2075c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 415a1

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	3	-	1	3	-6	-7	2	4	-7	5	-7	6	4	-4	-10	-3	5	2	14	-4	-14	+	12	8

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Quadratic twists for elliptic curve 415a1

-4	8	-3	5	-7	-11	13	17	-83
6640i1	26560e1	3735d1	2075c1	20335c1	50215c1	70135b1	119935b1	34445a1

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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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