Cremona's table of elliptic curves

20640 = 2⁵ · 3 · 5 · 43

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 43-	Signs for the Atkin-Lehner involutions
Class	20640b	Isogeny class
Conductor	20640	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	102144	Modular degree for the optimal curve
Δ	-257602680000000 = -1 · 29 · 34 · 57 · 433	Discriminant
Eigenvalues	2+ 3+ 5+  3 -4 -1  4 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-69256,-7034444]	[a1,a2,a3,a4,a6]
j	-71751706663500872/503130234375	j-invariant
L	1.7650378298615	L(r)(E,1)/r!
Ω	0.14708648582179	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	20640f1 41280dg1 61920cd1 103200cm1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 20640b1

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	-4	-1	4	-5	8	3	9	8	-3	-	-6	6	12	5	-15	6	-1	-1	-8	8	-14

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Quadratic twists for elliptic curve 20640b1

-4	8	-3	5
20640f1	41280dg1	61920cd1	103200cm1

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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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