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	12936k	Isogeny class
Conductor	12936	Conductor
∏ cp	36	Product of Tamagawa factors cp
deg	552960	Modular degree for the optimal curve
Δ	53035431305472 = 28 · 33 · 78 · 113	Discriminant
Eigenvalues	2+ 3- -2 7- 11-  6  2  8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-28761644,59360635872]	[a1,a2,a3,a4,a6]
j	87364831012240243408/1760913	j-invariant
L	2.9447978000527	L(r)(E,1)/r!
Ω	0.32719975556141	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	25872f1 103488x1 38808ce1 1848b1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12936k1

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

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Quadratic twists for elliptic curve 12936k1

-4	8	-3	-7
25872f1	103488x1	38808ce1	1848b1

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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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