Cremona's table of elliptic curves

153 = 3² · 17

Field	Data	Notes
Atkin-Lehner	3+ 17+	Signs for the Atkin-Lehner involutions
Class	153a	Isogeny class
Conductor	153	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	8	Modular degree for the optimal curve
Δ	-459 = -1 · 33 · 17	Discriminant
Eigenvalues	-2 3+ -1 -2 -3 -5 17+ -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-3,2]	[a1,a2,a3,a4,a6]
Generators	[0:1:1]	Generators of the group modulo torsion
j	-110592/17	j-invariant
L	0.7068417367258	L(r)(E,1)/r!
Ω	5.0866355583654	Real period
R	0.069480281083174	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	2448i1 9792a1 153d1 3825d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 153a1

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	-2	-3	-5	+	-1	-7	6	4	10	9	1	-12	-12	6	2	4	-8	0	-6	4	2	8

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Quadratic twists for elliptic curve 153a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29
2448i1	9792a1	153d1	3825d1	7497b1	18513f1	25857a1	2601d1	55233c1	80937d1	128673d1

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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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