Cremona's table of elliptic curves

29744 = 2⁴ · 11 · 13²

Field	Data	Notes
Atkin-Lehner	2- 11- 13+	Signs for the Atkin-Lehner involutions
Class	29744bg	Isogeny class
Conductor	29744	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	157248	Modular degree for the optimal curve
Δ	-294028506923008 = -1 · 215 · 11 · 138	Discriminant
Eigenvalues	2- -2 -4  2 11- 13+  8  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-9520,-902316]	[a1,a2,a3,a4,a6]
Generators	[130:272:1]	Generators of the group modulo torsion
j	-28561/88	j-invariant
L	3.0357740166618	L(r)(E,1)/r!
Ω	0.22312640994363	Real period
R	3.4014059759094	Regulator
r	1	Rank of the group of rational points
S	0.99999999999999	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3718m1 118976ch1 29744u1	Quadratic twists by: -4 8 13

Hecke Eigenvalues for elliptic curve 29744bg1

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	-4	2	-	+	8	1	-1	1	0	10	10	-11	1	-10	-14	-2	-8	3	-4	-8	-9	-1	-1

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Quadratic twists for elliptic curve 29744bg1

-4	8	13
3718m1	118976ch1	29744u1

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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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