Cremona's table of elliptic curves

12210 = 2 · 3 · 5 · 11 · 37

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 11- 37-	Signs for the Atkin-Lehner involutions
Class	12210y	Isogeny class
Conductor	12210	Conductor
∏ cp	625	Product of Tamagawa factors cp
deg	104000	Modular degree for the optimal curve
Δ	18535639706100000 = 25 · 35 · 55 · 11 · 375	Discriminant
Eigenvalues	2- 3- 5-  3 11- -1  3  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-130890,-17019900]	[a1,a2,a3,a4,a6]
j	247995227167710291361/18535639706100000	j-invariant
L	6.304633372602	L(r)(E,1)/r!
Ω	0.25218533490408	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	5	Number of elements in the torsion subgroup
Twists	97680br1 36630j1 61050h1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 12210y1

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
-	-	-	3	-	-1	3	0	4	-5	2	-	-3	9	3	-6	10	-8	3	2	-6	0	9	-15	-7

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Quadratic twists for elliptic curve 12210y1

-4	-3	5
97680br1	36630j1	61050h1

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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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