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	13272a	Isogeny class
Conductor	13272	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-365408502552576 = -1 · 211 · 35 · 76 · 792	Discriminant
Eigenvalues	2+ 3+ -2 7+  4 -4 -6  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,1336,-919956]	[a1,a2,a3,a4,a6]
Generators	[4172966:162705059:2744]	Generators of the group modulo torsion
j	128673176686/178422120387	j-invariant
L	3.1589542451629	L(r)(E,1)/r!
Ω	0.24984352661878	Real period
R	12.643730609771	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	26544g2 106176o2 39816g2 92904g2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 13272a2

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	-4	-6	6	4	-6	8	-4	10	-10	4	-14	4	-2	12	-2	-2	+	8	0	10

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Quadratic twists for elliptic curve 13272a2

-4	8	-3	-7
26544g2	106176o2	39816g2	92904g2

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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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