Cremona's table of elliptic curves

13072 = 2⁴ · 19 · 43

Field	Data	Notes
Atkin-Lehner	2- 19- 43+	Signs for the Atkin-Lehner involutions
Class	13072g	Isogeny class
Conductor	13072	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	4032	Modular degree for the optimal curve
Δ	-63582208 = -1 · 212 · 192 · 43	Discriminant
Eigenvalues	2-  2 -2  4  5 -3 -3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,11,-387]	[a1,a2,a3,a4,a6]
Generators	[36:213:1]	Generators of the group modulo torsion
j	32768/15523	j-invariant
L	6.8005956131408	L(r)(E,1)/r!
Ω	0.91964304421163	Real period
R	3.6974104550373	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	817a1 52288s1 117648by1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 13072g1

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	-2	4	5	-3	-3	-	-3	-4	3	-8	-5	+	-8	-7	4	2	-7	-4	-10	4	-3	-16	1

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Quadratic twists for elliptic curve 13072g1

-4	8	-3
817a1	52288s1	117648by1

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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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