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	29744v	Isogeny class
Conductor	29744	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	7200	Modular degree for the optimal curve
Δ	4253392 = 24 · 112 · 133	Discriminant
Eigenvalues	2-  0  0  4 11+ 13-  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-520,4563]	[a1,a2,a3,a4,a6]
Generators	[-23:66:1]	Generators of the group modulo torsion
j	442368000/121	j-invariant
L	5.8017668316561	L(r)(E,1)/r!
Ω	2.404573808432	Real period
R	2.412804635612	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	7436d1 118976dp1 29744bh1	Quadratic twists by: -4 8 13

Hecke Eigenvalues for elliptic curve 29744v1

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
-	0	0	4	+	-	2	-4	-4	-6	4	-8	12	12	-4	6	4	-10	-4	4	-4	8	12	16	8

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Quadratic twists for elliptic curve 29744v1

-4	8	13
7436d1	118976dp1	29744bh1

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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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