Cremona's table of elliptic curves

12642 = 2 · 3 · 7² · 43

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 43-	Signs for the Atkin-Lehner involutions
Class	12642bm	Isogeny class
Conductor	12642	Conductor
∏ cp	1020	Product of Tamagawa factors cp
deg	195840	Modular degree for the optimal curve
Δ	2085488727443767296 = 217 · 35 · 77 · 433	Discriminant
Eigenvalues	2- 3- -1 7- -4  3  1  1	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-538511,135262329]	[a1,a2,a3,a4,a6]
Generators	[-710:12997:1]	Generators of the group modulo torsion
j	146797702716641761/17726361698304	j-invariant
L	7.8317532722624	L(r)(E,1)/r!
Ω	0.2522922980298	Real period
R	0.030433705438378	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	101136bc1 37926w1 1806i1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 12642bm1

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	-	-4	3	1	1	-1	-8	3	-1	-9	-	-6	-3	11	0	-5	-10	2	-6	4	-18	2

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Quadratic twists for elliptic curve 12642bm1

-4	-3	-7
101136bc1	37926w1	1806i1

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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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