Cremona's table of elliptic curves

23064 = 2³ · 3 · 31²

Field	Data	Notes
Atkin-Lehner	2+ 3+ 31+	Signs for the Atkin-Lehner involutions
Class	23064a	Isogeny class
Conductor	23064	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	193440	Modular degree for the optimal curve
Δ	-5240162534037504 = -1 · 211 · 3 · 318	Discriminant
Eigenvalues	2+ 3+  2 -5  3  0  6  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-69512,-7843860]	[a1,a2,a3,a4,a6]
Generators	[15401355153396566999:23859749567894890330:49734938705665751]	Generators of the group modulo torsion
j	-21266/3	j-invariant
L	4.6347751180163	L(r)(E,1)/r!
Ω	0.14587077879295	Real period
R	31.773156737545	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	46128j1 69192be1 23064g1	Quadratic twists by: -4 -3 -31

Hecke Eigenvalues for elliptic curve 23064a1

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
+	+	2	-5	3	0	6	6	0	-3	+	-8	4	-8	6	1	-11	-8	-12	-16	2	-8	11	-2	19

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Quadratic twists for elliptic curve 23064a1

-4	-3	-31
46128j1	69192be1	23064g1

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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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