Cremona's table of elliptic curves

416 = 2⁵ · 13

Field	Data	Notes
Atkin-Lehner	2+ 13-	Signs for the Atkin-Lehner involutions
Class	416a	Isogeny class
Conductor	416	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	16	Modular degree for the optimal curve
Δ	-6656 = -1 · 29 · 13	Discriminant
Eigenvalues	2+  1  1  3  2 13- -3  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,0,-4]	[a1,a2,a3,a4,a6]
j	-8/13	j-invariant
L	1.9071354956947	L(r)(E,1)/r!
Ω	1.9071354956947	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	416b1 832b1 3744o1 10400u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 416a1

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

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Quadratic twists for elliptic curve 416a1

-4	8	-3	5	-7	-11	13	17
416b1	832b1	3744o1	10400u1	20384f1	50336s1	5408h1	120224a1

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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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