Cremona's table of elliptic curves

11872 = 2⁵ · 7 · 53

Field	Data	Notes
Atkin-Lehner	2+ 7+ 53-	Signs for the Atkin-Lehner involutions
Class	11872a	Isogeny class
Conductor	11872	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	3192523264 = 29 · 76 · 53	Discriminant
Eigenvalues	2+  0 -2 7+  0  0 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-451,-2490]	[a1,a2,a3,a4,a6]
Generators	[-15:30:1] [-7:18:1]	Generators of the group modulo torsion
j	19814511816/6235397	j-invariant
L	5.5761579390064	L(r)(E,1)/r!
Ω	1.0616220292836	Real period
R	5.2524889133741	Regulator
r	2	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	11872c2 23744u2 106848ba2 83104c2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 11872a2

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

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Quadratic twists for elliptic curve 11872a2

-4	8	-3	-7
11872c2	23744u2	106848ba2	83104c2

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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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