Cremona's table of elliptic curves

12546 = 2 · 3² · 17 · 41

Field	Data	Notes
Atkin-Lehner	2+ 3- 17- 41-	Signs for the Atkin-Lehner involutions
Class	12546h	Isogeny class
Conductor	12546	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	19050692903712 = 25 · 36 · 172 · 414	Discriminant
Eigenvalues	2+ 3- -4  0 -2 -2 17- -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-6894,68404]	[a1,a2,a3,a4,a6]
Generators	[3:217:1] [5:182:1]	Generators of the group modulo torsion
j	49710193744609/26132637728	j-invariant
L	4.0301175068192	L(r)(E,1)/r!
Ω	0.60312106315268	Real period
R	1.6705259329503	Regulator
r	2	Rank of the group of rational points
S	0.99999999999967	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	100368cg2 1394f2	Quadratic twists by: -4 -3

Hecke Eigenvalues for elliptic curve 12546h2

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
+	-	-4	0	-2	-2	-	-8	4	-8	-8	0	-	-8	0	2	-8	0	4	-12	2	-4	0	-10	-2

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Quadratic twists for elliptic curve 12546h2

-4	-3
100368cg2	1394f2

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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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