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
deg	28800	Modular degree for the optimal curve
Δ	1638451971072 = 210 · 310 · 73 · 79	Discriminant
Eigenvalues	2+ 3+ -2 7+  4 -4 -6  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-8384,-286212]	[a1,a2,a3,a4,a6]
Generators	[1522:59248:1]	Generators of the group modulo torsion
j	63654537026308/1600050753	j-invariant
L	3.1589542451629	L(r)(E,1)/r!
Ω	0.49968705323756	Real period
R	6.3218653048853	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	26544g1 106176o1 39816g1 92904g1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 13272a1

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 13272a1

-4	8	-3	-7
26544g1	106176o1	39816g1	92904g1

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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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