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	12	Product of Tamagawa factors cp
Δ	-10744731 = -1 · 37 · 173	Discriminant
Eigenvalues	0 3- -3 -4  3 -1 17- -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-534,4752]	[a1,a2,a3,a4,a6]
Generators	[-22:76:1]	Generators of the group modulo torsion
j	-23100424192/14739	j-invariant
L	1.0181559606614	L(r)(E,1)/r!
Ω	2.2547575496567	Real period
R	0.33866921550492	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	2448s2 9792y2 51a2 3825e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 153b2

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 153b2

-4	8	-3	5	-7	-11	13	17	-19	-23	29
2448s2	9792y2	51a2	3825e2	7497f2	18513n2	25857q2	2601g2	55233p2	80937i2	128673e2

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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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