Cremona's table of elliptic curves

12936 = 2³ · 3 · 7² · 11

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 11+	Signs for the Atkin-Lehner involutions
Class	12936n	Isogeny class
Conductor	12936	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	343033169683792896 = 210 · 34 · 710 · 114	Discriminant
Eigenvalues	2- 3+  2 7- 11+  2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-181512,9647100]	[a1,a2,a3,a4,a6]
Generators	[195984:4235805:4096]	Generators of the group modulo torsion
j	5489767279588/2847396321	j-invariant
L	4.5634407732481	L(r)(E,1)/r!
Ω	0.26722033761485	Real period
R	8.5387227895532	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	25872w4 103488eb4 38808bg4 1848j3	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12936n3

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	-	+	2	-2	-4	0	6	8	-10	6	-12	8	-10	-12	2	-4	0	6	0	12	-10	14

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Quadratic twists for elliptic curve 12936n3

-4	8	-3	-7
25872w4	103488eb4	38808bg4	1848j3

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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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