Cremona's table of elliptic curves

1615 = 5 · 17 · 19

Field	Data	Notes
Atkin-Lehner	5- 17+ 19-	Signs for the Atkin-Lehner involutions
Class	1615b	Isogeny class
Conductor	1615	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	448	Modular degree for the optimal curve
Δ	-126171875 = -1 · 58 · 17 · 19	Discriminant
Eigenvalues	0 -1 5-  4 -2 -2 17+ 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-305,-2022]	[a1,a2,a3,a4,a6]
Generators	[24:62:1]	Generators of the group modulo torsion
j	-3148084412416/126171875	j-invariant
L	2.2953817289526	L(r)(E,1)/r!
Ω	0.56971436386988	Real period
R	0.5036255610094	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	25840z1 103360b1 14535k1 8075e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1615b1

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	-1	-	4	-2	-2	+	-	-8	3	3	2	-6	-1	-3	-6	-2	-6	-14	-8	14	0	-11	-14	-11

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Quadratic twists for elliptic curve 1615b1

-4	8	-3	5	-7	17	-19
25840z1	103360b1	14535k1	8075e1	79135n1	27455c1	30685d1

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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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