Cremona's table of elliptic curves

242 = 2 · 11²

Field	Data	Notes
Atkin-Lehner	2- 11-	Signs for the Atkin-Lehner involutions
Class	242a	Isogeny class
Conductor	242	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	16	Modular degree for the optimal curve
Δ	-1936 = -1 · 24 · 112	Discriminant
Eigenvalues	2- -2 -3 -2 11- -5 -3 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,3,1]	[a1,a2,a3,a4,a6]
Generators	[0:1:1]	Generators of the group modulo torsion
j	24167/16	j-invariant
L	1.4486447783624	L(r)(E,1)/r!
Ω	2.9307853161438	Real period
R	0.12357138293128	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	1936i1 7744k1 2178f1 6050j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 242a1

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	-3	-2	-	-5	-3	-2	6	3	2	-7	-3	-8	6	-3	0	10	-10	12	-14	-2	-18	-9	11

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Quadratic twists for elliptic curve 242a1

-4	8	-3	5	-7	-11	13	17	-19	-23
1936i1	7744k1	2178f1	6050j1	11858bl1	242b1	40898s1	69938q1	87362t1	128018bd1

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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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