Cremona's table of elliptic curves

12274 = 2 · 17 · 19²

Field	Data	Notes
Atkin-Lehner	2+ 17+ 19-	Signs for the Atkin-Lehner involutions
Class	12274c	Isogeny class
Conductor	12274	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1440	Modular degree for the optimal curve
Δ	-208658 = -1 · 2 · 172 · 192	Discriminant
Eigenvalues	2+ -1 -2 -2 -1  0 17+ 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-26,46]	[a1,a2,a3,a4,a6]
Generators	[-1:9:1] [5:6:1]	Generators of the group modulo torsion
j	-5714497/578	j-invariant
L	3.5605249179396	L(r)(E,1)/r!
Ω	3.0861026915537	Real period
R	0.57686429678535	Regulator
r	2	Rank of the group of rational points
S	0.99999999999962	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	98192m1 110466br1 12274j1	Quadratic twists by: -4 -3 -19

Hecke Eigenvalues for elliptic curve 12274c1

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
+	-1	-2	-2	-1	0	+	-	-6	8	-8	-2	5	12	-2	-12	-9	-8	-11	-6	-15	-14	17	-6	1

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Quadratic twists for elliptic curve 12274c1

-4	-3	-19
98192m1	110466br1	12274j1

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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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