Cremona's table of elliptic curves

8736 = 2⁵ · 3 · 7 · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 13-	Signs for the Atkin-Lehner involutions
Class	8736ba	Isogeny class
Conductor	8736	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	271724544 = 212 · 36 · 7 · 13	Discriminant
Eigenvalues	2- 3- -2 7- -4 13-  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-449,-3729]	[a1,a2,a3,a4,a6]
Generators	[-14:3:1]	Generators of the group modulo torsion
j	2449456192/66339	j-invariant
L	4.5698413093755	L(r)(E,1)/r!
Ω	1.0386651006873	Real period
R	1.4665751602229	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	8736p2 17472cd1 26208v2 61152be2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 8736ba2

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	-	-4	-	0	4	-2	-6	0	10	-2	4	6	2	-6	10	4	0	-10	-12	-14	-14	-14

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Quadratic twists for elliptic curve 8736ba2

-4	8	-3	-7	13
8736p2	17472cd1	26208v2	61152be2	113568bb2

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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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