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	1872q	Isogeny class
Conductor	1872	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	512	Modular degree for the optimal curve
Δ	-116453376 = -1 · 212 · 37 · 13	Discriminant
Eigenvalues	2- 3- -2  4  4 13- -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,69,-470]	[a1,a2,a3,a4,a6]
j	12167/39	j-invariant
L	1.9091538124883	L(r)(E,1)/r!
Ω	0.95457690624414	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	117a1 7488bs1 624h1 46800dm1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1872q1

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	-	-2	0	0	10	-4	-2	-6	12	0	-6	12	-2	8	0	2	-8	4	2	10

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Quadratic twists for elliptic curve 1872q1

-4	8	-3	5	-7	13
117a1	7488bs1	624h1	46800dm1	91728ef1	24336bt1

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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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