Cremona's table of elliptic curves

38440 = 2³ · 5 · 31²

Field	Data	Notes
Atkin-Lehner	2+ 5+ 31+	Signs for the Atkin-Lehner involutions
Class	38440a	Isogeny class
Conductor	38440	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	193440	Modular degree for the optimal curve
Δ	1091700527924480 = 28 · 5 · 318	Discriminant
Eigenvalues	2+  2 5+ -2  3  4  6  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-39721,2612781]	[a1,a2,a3,a4,a6]
Generators	[153:306:1]	Generators of the group modulo torsion
j	31744/5	j-invariant
L	7.999408484863	L(r)(E,1)/r!
Ω	0.46914551793694	Real period
R	4.2627544008314	Regulator
r	1	Rank of the group of rational points
S	0.99999999999987	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	76880a1 38440d1	Quadratic twists by: -4 -31

Hecke Eigenvalues for elliptic curve 38440a1

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	+	-2	3	4	6	0	-4	-7	+	8	5	-10	-10	-4	-9	13	12	-7	-6	1	4	-15	-8

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Quadratic twists for elliptic curve 38440a1

-4	-31
76880a1	38440d1

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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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