Cremona's table of elliptic curves

1936 = 2⁴ · 11²

Field	Data	Notes
Atkin-Lehner	2- 11-	Signs for the Atkin-Lehner involutions
Class	1936l	Isogeny class
Conductor	1936	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-495616 = -1 · 212 · 112	Discriminant
Eigenvalues	2- -2  1 -2 11- -1  5  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-480,3892]	[a1,a2,a3,a4,a6]
Generators	[12:2:1]	Generators of the group modulo torsion
j	-24729001	j-invariant
L	2.1977641007139	L(r)(E,1)/r!
Ω	2.7630086734008	Real period
R	0.39771212480647	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	121a1 7744bc1 17424bu1 48400cg1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1936l1

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	1	-2	-	-1	5	6	-2	-9	2	-3	5	0	-2	9	-8	-6	-2	-12	2	-10	6	-9	-13

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Quadratic twists for elliptic curve 1936l1

-4	8	-3	5	-7	-11
121a1	7744bc1	17424bu1	48400cg1	94864cq1	1936k2

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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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