Cremona's table of elliptic curves

1872 = 2⁴ · 3² · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 13+	Signs for the Atkin-Lehner involutions
Class	1872o	Isogeny class
Conductor	1872	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	151632 = 24 · 36 · 13	Discriminant
Eigenvalues	2- 3- -2  2 -2 13+ -6  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-36,-81]	[a1,a2,a3,a4,a6]
Generators	[9:18:1]	Generators of the group modulo torsion
j	442368/13	j-invariant
L	2.7779265892338	L(r)(E,1)/r!
Ω	1.9525598324275	Real period
R	1.4227100973291	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	468c1 7488cb1 208c2 46800eb1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1872o1

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	-2	+	-6	6	8	-2	-10	-6	6	-4	-2	-6	-10	-2	-10	10	2	4	-6	6	2

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Quadratic twists for elliptic curve 1872o1

-4	8	-3	5	-7	13
468c1	7488cb1	208c2	46800eb1	91728fm1	24336br1

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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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