Cremona's table of elliptic curves

13272 = 2³ · 3 · 7 · 79

Field	Data	Notes
Atkin-Lehner	2+ 3- 7- 79+	Signs for the Atkin-Lehner involutions
Class	13272c	Isogeny class
Conductor	13272	Conductor
∏ cp	28	Product of Tamagawa factors cp
Δ	677115355392 = 28 · 314 · 7 · 79	Discriminant
Eigenvalues	2+ 3- -4 7-  4 -6  6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2220,6624]	[a1,a2,a3,a4,a6]
Generators	[-24:216:1]	Generators of the group modulo torsion
j	4728662124496/2644981857	j-invariant
L	4.3979289243125	L(r)(E,1)/r!
Ω	0.78441257154879	Real period
R	0.80095039702841	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	26544b2 106176i2 39816j2 92904d2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 13272c2

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
+	-	-4	-	4	-6	6	-8	-4	4	-4	-2	6	8	8	0	0	-2	4	-6	6	+	-18	-8	14

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Quadratic twists for elliptic curve 13272c2

-4	8	-3	-7
26544b2	106176i2	39816j2	92904d2

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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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