Cremona's table of elliptic curves

153 = 3² · 17

Field	Data	Notes
Atkin-Lehner	3- 17-	Signs for the Atkin-Lehner involutions
Class	153b	Isogeny class
Conductor	153	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	16	Modular degree for the optimal curve
Δ	-334611 = -1 · 39 · 17	Discriminant
Eigenvalues	0 3- -3 -4  3 -1 17- -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,6,27]	[a1,a2,a3,a4,a6]
Generators	[5:13:1]	Generators of the group modulo torsion
j	32768/459	j-invariant
L	1.0181559606614	L(r)(E,1)/r!
Ω	2.2547575496567	Real period
R	0.11288973850164	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	2448s1 9792y1 51a1 3825e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 153b1

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	-	-3	-4	3	-1	-	-1	-9	-6	2	-4	3	-7	6	6	-6	8	-4	-12	2	-10	6	0	-16

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Quadratic twists for elliptic curve 153b1

-4	8	-3	5	-7	-11	13	17	-19	-23	29
2448s1	9792y1	51a1	3825e1	7497f1	18513n1	25857q1	2601g1	55233p1	80937i1	128673e1

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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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