Cremona's table of elliptic curves

13940 = 2² · 5 · 17 · 41

Field	Data	Notes
Atkin-Lehner	2- 5+ 17+ 41+	Signs for the Atkin-Lehner involutions
Class	13940a	Isogeny class
Conductor	13940	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	55680	Modular degree for the optimal curve
Δ	18880830758480 = 24 · 5 · 174 · 414	Discriminant
Eigenvalues	2-  2 5+ -2  0 -2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-138641,19914626]	[a1,a2,a3,a4,a6]
j	18419672688642310144/1180051922405	j-invariant
L	1.956666991744	L(r)(E,1)/r!
Ω	0.65222233058132	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	55760k1 125460w1 69700l1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 13940a1

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	0	-2	+	-4	6	-2	4	-6	+	6	-2	-2	12	2	14	4	-14	0	-2	-14	14

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Quadratic twists for elliptic curve 13940a1

-4	-3	5
55760k1	125460w1	69700l1

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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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