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	12210n	Isogeny class
Conductor	12210	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	9216	Modular degree for the optimal curve
Δ	464175360 = 28 · 34 · 5 · 112 · 37	Discriminant
Eigenvalues	2+ 3- 5+  2 11+  6  6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-254,1136]	[a1,a2,a3,a4,a6]
Generators	[-6:52:1]	Generators of the group modulo torsion
j	1802041022809/464175360	j-invariant
L	4.3961684270863	L(r)(E,1)/r!
Ω	1.5582040345284	Real period
R	0.70532618477285	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	97680bf1 36630br1 61050bm1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 12210n1

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	+	6	6	-2	-8	-8	-8	-	-2	-8	8	6	0	-12	4	-16	4	2	-10	-6	18

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Quadratic twists for elliptic curve 12210n1

-4	-3	5
97680bf1	36630br1	61050bm1

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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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