Cremona's table of elliptic curves

23664 = 2⁴ · 3 · 17 · 29

Field	Data	Notes
Atkin-Lehner	2+ 3+ 17- 29-	Signs for the Atkin-Lehner involutions
Class	23664d	Isogeny class
Conductor	23664	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	75264	Modular degree for the optimal curve
Δ	-2313297605376 = -1 · 28 · 37 · 173 · 292	Discriminant
Eigenvalues	2+ 3+ -3  2  5 -5 17-  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-21697,-1225091]	[a1,a2,a3,a4,a6]
Generators	[1386:3451:8]	Generators of the group modulo torsion
j	-4412684020139008/9036318771	j-invariant
L	3.9726449523568	L(r)(E,1)/r!
Ω	0.19665938502782	Real period
R	3.3667729204268	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	11832c1 94656cb1 70992c1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 23664d1

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
+	+	-3	2	5	-5	-	1	7	-	4	-10	-3	11	2	-6	0	-12	-12	-8	14	-14	0	-6	-10

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Quadratic twists for elliptic curve 23664d1

-4	8	-3
11832c1	94656cb1	70992c1

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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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