Cremona's table of elliptic curves

1573 = 11² · 13

Field	Data	Notes
Atkin-Lehner	11- 13-	Signs for the Atkin-Lehner involutions
Class	1573b	Isogeny class
Conductor	1573	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	-3293331899 = -1 · 117 · 132	Discriminant
Eigenvalues	0 -1 -1  2 11- 13-  4 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-161,2925]	[a1,a2,a3,a4,a6]
Generators	[-7:60:1]	Generators of the group modulo torsion
j	-262144/1859	j-invariant
L	1.9961126953954	L(r)(E,1)/r!
Ω	1.2155564474659	Real period
R	0.20526737976225	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	25168bh1 100672i1 14157q1 39325a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1573b1

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	-1	2	-	-	4	-2	7	2	-3	-11	-10	4	-4	2	-1	2	-1	-9	16	-8	0	-7	-13

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Quadratic twists for elliptic curve 1573b1

-4	8	-3	5	-7	-11	13
25168bh1	100672i1	14157q1	39325a1	77077i1	143a1	20449b1

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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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