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	1872i	Isogeny class
Conductor	1872	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	283855104 = 28 · 38 · 132	Discriminant
Eigenvalues	2+ 3- -2  0  0 13- -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-471,-3850]	[a1,a2,a3,a4,a6]
Generators	[38:182:1]	Generators of the group modulo torsion
j	61918288/1521	j-invariant
L	2.7085124774504	L(r)(E,1)/r!
Ω	1.0263479457208	Real period
R	2.6389807557398	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	936e2 7488br2 624c2 46800k2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1872i2

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	0	0	-	-2	4	0	-6	0	-2	-6	12	-4	-6	-8	-2	-4	-12	-14	0	8	18	-6

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Quadratic twists for elliptic curve 1872i2

-4	8	-3	5	-7	13
936e2	7488br2	624c2	46800k2	91728w2	24336f2

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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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