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	1872t	Isogeny class
Conductor	1872	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	1364688 = 24 · 38 · 13	Discriminant
Eigenvalues	2- 3-  4  2 -4 13- -2  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-48,115]	[a1,a2,a3,a4,a6]
j	1048576/117	j-invariant
L	2.6201543024438	L(r)(E,1)/r!
Ω	2.6201543024438	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	468e1 7488bw1 624j1 46800df1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1872t1

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

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Quadratic twists for elliptic curve 1872t1

-4	8	-3	5	-7	13
468e1	7488bw1	624j1	46800df1	91728ev1	24336cb1

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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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