Cremona's table of elliptic curves

38720 = 2⁶ · 5 · 11²

Field	Data	Notes
Atkin-Lehner	2- 5+ 11-	Signs for the Atkin-Lehner involutions
Class	38720ca	Isogeny class
Conductor	38720	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	202752	Modular degree for the optimal curve
Δ	-4495431560069120 = -1 · 222 · 5 · 118	Discriminant
Eigenvalues	2- -1 5+  3 11-  0  8  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-19521,3398881]	[a1,a2,a3,a4,a6]
Generators	[453:9344:1]	Generators of the group modulo torsion
j	-14641/80	j-invariant
L	5.2947969141557	L(r)(E,1)/r!
Ω	0.37699110874658	Real period
R	3.5112213466784	Regulator
r	1	Rank of the group of rational points
S	0.99999999999996	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	38720k1 9680x1 38720cd1	Quadratic twists by: -4 8 -11

Hecke Eigenvalues for elliptic curve 38720ca1

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	-	0	8	8	0	-2	-6	0	5	1	5	-8	-10	-7	-7	14	-16	-10	-12	9	12

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Quadratic twists for elliptic curve 38720ca1

-4	8	-11
38720k1	9680x1	38720cd1

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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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