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	12936i	Isogeny class
Conductor	12936	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	13824	Modular degree for the optimal curve
Δ	-473530636656 = -1 · 24 · 33 · 77 · 113	Discriminant
Eigenvalues	2+ 3-  1 7- 11+  3 -4 -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-11580,476937]	[a1,a2,a3,a4,a6]
Generators	[72:-147:1]	Generators of the group modulo torsion
j	-91238612224/251559	j-invariant
L	6.1182863991653	L(r)(E,1)/r!
Ω	0.93765186478041	Real period
R	0.2718797983993	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	25872j1 103488bv1 38808ci1 1848a1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12936i1

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	-	+	3	-4	-1	2	-1	-4	-3	-4	2	-5	2	-9	2	-3	12	-7	-8	-12	2	-10

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Quadratic twists for elliptic curve 12936i1

-4	8	-3	-7
25872j1	103488bv1	38808ci1	1848a1

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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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