Cremona's table of elliptic curves

12100 = 2² · 5² · 11²

Field	Data	Notes
Atkin-Lehner	2- 5+ 11-	Signs for the Atkin-Lehner involutions
Class	12100f	Isogeny class
Conductor	12100	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	55361281250000 = 24 · 59 · 116	Discriminant
Eigenvalues	2-  2 5+  2 11-  2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-125033,17055062]	[a1,a2,a3,a4,a6]
Generators	[-37218:1249325:216]	Generators of the group modulo torsion
j	488095744/125	j-invariant
L	6.9260401107067	L(r)(E,1)/r!
Ω	0.61329674576488	Real period
R	5.6465651893105	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	48400cn3 108900bx3 2420e3 100a3	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 12100f3

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

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Quadratic twists for elliptic curve 12100f3

-4	-3	5	-11
48400cn3	108900bx3	2420e3	100a3

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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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