Cremona's table of elliptic curves

7569 = 3² · 29²

Field	Data	Notes
Atkin-Lehner	3+ 29+	Signs for the Atkin-Lehner involutions
Class	7569a	Isogeny class
Conductor	7569	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	22040	Modular degree for the optimal curve
Δ	-11359095299105427 = -1 · 33 · 2910	Discriminant
Eigenvalues	0 3+  0 -1  0  2  0  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,0,5127787]	[a1,a2,a3,a4,a6]
Generators	[115:2578:1]	Generators of the group modulo torsion
j	0	j-invariant
L	3.2989913022992	L(r)(E,1)/r!
Ω	0.3203347168771	Real period
R	5.1492878050506	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	121104ba1 7569a2 7569b1	Quadratic twists by: -4 -3 29

Hecke Eigenvalues for elliptic curve 7569a1

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	+	0	-1	0	2	0	1	0	+	4	-11	0	-5	0	0	0	13	11	0	10	13	0	0	-14

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Quadratic twists for elliptic curve 7569a1

-4	-3	29
121104ba1	7569a2	7569b1

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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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