Cremona's table of elliptic curves

13664 = 2⁵ · 7 · 61

Field	Data	Notes
Atkin-Lehner	2- 7- 61-	Signs for the Atkin-Lehner involutions
Class	13664h	Isogeny class
Conductor	13664	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	24320	Modular degree for the optimal curve
Δ	4199329792 = 212 · 75 · 61	Discriminant
Eigenvalues	2- -3 -4 7- -3  0 -7  5	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-412,-800]	[a1,a2,a3,a4,a6]
Generators	[-18:28:1] [-11:49:1]	Generators of the group modulo torsion
j	1888232256/1025227	j-invariant
L	3.4781685339862	L(r)(E,1)/r!
Ω	1.1301100383328	Real period
R	0.15388627726547	Regulator
r	2	Rank of the group of rational points
S	0.99999999999959	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13664d1 27328j1 122976o1 95648q1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 13664h1

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	-	-3	0	-7	5	-9	-6	8	-6	2	-9	3	10	-2	-	-13	-9	10	11	-11	1	-6

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Quadratic twists for elliptic curve 13664h1

-4	8	-3	-7
13664d1	27328j1	122976o1	95648q1

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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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