Cremona's table of elliptic curves

469 = 7 · 67

Field	Data	Notes
Atkin-Lehner	7+ 67+	Signs for the Atkin-Lehner involutions
Class	469b	Isogeny class
Conductor	469	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	32	Modular degree for the optimal curve
Δ	469 = 7 · 67	Discriminant
Eigenvalues	-1 -3  1 7+  0  3  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-12,18]	[a1,a2,a3,a4,a6]
Generators	[2:-1:1]	Generators of the group modulo torsion
j	176558481/469	j-invariant
L	0.90968912826427	L(r)(E,1)/r!
Ω	5.2760385038547	Real period
R	0.17241897071063	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	7504u1 30016l1 4221a1 11725b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 469b1

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
-1	-3	1	+	0	3	0	-4	3	-3	-5	5	-5	0	-6	2	-6	-14	+	-9	14	14	-10	4	2

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Quadratic twists for elliptic curve 469b1

-4	8	-3	5	-7	-11	13	-67
7504u1	30016l1	4221a1	11725b1	3283d1	56749d1	79261e1	31423b1

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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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