Cremona's table of elliptic curves

1936 = 2⁴ · 11²

Field	Data	Notes
Atkin-Lehner	2+ 11+	Signs for the Atkin-Lehner involutions
Class	1936a	Isogeny class
Conductor	1936	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-340736 = -1 · 28 · 113	Discriminant
Eigenvalues	2+ -1  1  4 11+ -4 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,15,13]	[a1,a2,a3,a4,a6]
Generators	[4:11:1]	Generators of the group modulo torsion
j	1024	j-invariant
L	2.8422615967817	L(r)(E,1)/r!
Ω	1.9972350524386	Real period
R	0.71154909716594	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	968a1 7744q1 17424g1 48400d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1936a1

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	1	4	+	-4	-4	-4	3	-8	-9	-5	12	8	-4	-10	-7	8	-11	9	-4	8	0	-1	1

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Quadratic twists for elliptic curve 1936a1

-4	8	-3	5	-7	-11
968a1	7744q1	17424g1	48400d1	94864h1	1936b1

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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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