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	1872j	Isogeny class
Conductor	1872	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	54500179968 = 214 · 39 · 132	Discriminant
Eigenvalues	2- 3+  2  2 -4 13+  0  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-9099,333882]	[a1,a2,a3,a4,a6]
j	1033364331/676	j-invariant
L	2.2156960427532	L(r)(E,1)/r!
Ω	1.1078480213766	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	234b2 7488bi2 1872k2 46800cm2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1872j2

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	+	0	6	4	8	2	6	-6	8	8	-12	4	10	2	-16	14	4	-12	6	-10

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Quadratic twists for elliptic curve 1872j2

-4	8	-3	5	-7	13
234b2	7488bi2	1872k2	46800cm2	91728cx2	24336be2

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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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