Cremona's table of elliptic curves

1936 = 2⁴ · 11²

Field	Data	Notes
Atkin-Lehner	2- 11-	Signs for the Atkin-Lehner involutions
Class	1936k	Isogeny class
Conductor	1936	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-59969536 = -1 · 212 · 114	Discriminant
Eigenvalues	2- -2  1  2 11-  1 -5 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-40,372]	[a1,a2,a3,a4,a6]
Generators	[-4:22:1]	Generators of the group modulo torsion
j	-121	j-invariant
L	2.4050040326561	L(r)(E,1)/r!
Ω	1.6911384598331	Real period
R	0.23702021742338	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	121c1 7744bb1 17424bt1 48400ch1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1936k1

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 1936k1

-4	8	-3	5	-7	-11
121c1	7744bb1	17424bt1	48400ch1	94864cr1	1936l2

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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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