Cremona's table of elliptic curves

29040 = 2⁴ · 3 · 5 · 11²

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5- 11-	Signs for the Atkin-Lehner involutions
Class	29040n	Isogeny class
Conductor	29040	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	61440	Modular degree for the optimal curve
Δ	-51142131572400 = -1 · 24 · 38 · 52 · 117	Discriminant
Eigenvalues	2+ 3+ 5-  0 11-  2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,7825,-220350]	[a1,a2,a3,a4,a6]
Generators	[170000:1709505:4096]	Generators of the group modulo torsion
j	1869154304/1804275	j-invariant
L	5.0008452335784	L(r)(E,1)/r!
Ω	0.34516074683115	Real period
R	7.2442264647561	Regulator
r	1	Rank of the group of rational points
S	0.99999999999999	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	14520u1 116160hr1 87120s1 2640f1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 29040n1

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	-	2	-2	4	-8	2	-8	6	-2	-4	0	6	-4	10	12	0	-2	8	12	-6	-14

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Quadratic twists for elliptic curve 29040n1

-4	8	-3	-11
14520u1	116160hr1	87120s1	2640f1

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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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