Cremona's table of elliptic curves

20384 = 2⁵ · 7² · 13

Field	Data	Notes
Atkin-Lehner	2+ 7- 13-	Signs for the Atkin-Lehner involutions
Class	20384v	Isogeny class
Conductor	20384	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	80640	Modular degree for the optimal curve
Δ	-45392319784448 = -1 · 29 · 79 · 133	Discriminant
Eigenvalues	2+ -3 -2 7-  3 13- -4  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-12691,-638666]	[a1,a2,a3,a4,a6]
Generators	[441:8918:1]	Generators of the group modulo torsion
j	-10941048/2197	j-invariant
L	2.4254366910521	L(r)(E,1)/r!
Ω	0.22249705087577	Real period
R	0.90841529565797	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	20384u1 40768dc1 20384n1	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 20384v1

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	-	3	-	-4	0	-3	-2	3	11	5	6	3	2	-12	-9	3	-6	-7	-9	6	2	-17

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Quadratic twists for elliptic curve 20384v1

-4	8	-7
20384u1	40768dc1	20384n1

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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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