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	1872l	Isogeny class
Conductor	1872	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-12338352 = -1 · 24 · 33 · 134	Discriminant
Eigenvalues	2- 3+  4 -4  4 13+  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-168,855]	[a1,a2,a3,a4,a6]
j	-1213857792/28561	j-invariant
L	2.2497620441206	L(r)(E,1)/r!
Ω	2.2497620441206	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	468a1 7488bl1 1872m1 46800cn1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1872l1

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

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Quadratic twists for elliptic curve 1872l1

-4	8	-3	5	-7	13
468a1	7488bl1	1872m1	46800cn1	91728dc1	24336bg1

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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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