Cremona's table of elliptic curves

14112 = 2⁵ · 3² · 7²

Field	Data	Notes
Atkin-Lehner	2+ 3- 7-	Signs for the Atkin-Lehner involutions
Class	14112s	Isogeny class
Conductor	14112	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	24576	Modular degree for the optimal curve
Δ	21785966991936 = 26 · 310 · 78	Discriminant
Eigenvalues	2+ 3-  2 7-  0 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-9849,-301840]	[a1,a2,a3,a4,a6]
Generators	[5124:58310:27]	Generators of the group modulo torsion
j	19248832/3969	j-invariant
L	5.59238212701	L(r)(E,1)/r!
Ω	0.48619072825827	Real period
R	5.7512225161556	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	14112t1 28224fz2 4704v1 2016h1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 14112s1

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	-2	2	4	0	-6	0	6	-6	-8	-8	-6	12	-10	-16	-8	6	-8	12	-14	6

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Quadratic twists for elliptic curve 14112s1

-4	8	-3	-7
14112t1	28224fz2	4704v1	2016h1

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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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