Cremona's table of elliptic curves

29760 = 2⁶ · 3 · 5 · 31

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 31-	Signs for the Atkin-Lehner involutions
Class	29760bt	Isogeny class
Conductor	29760	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	-73804800 = -1 · 210 · 3 · 52 · 312	Discriminant
Eigenvalues	2- 3+ 5+  0  0  2 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,59,-395]	[a1,a2,a3,a4,a6]
Generators	[9:28:1]	Generators of the group modulo torsion
j	21807104/72075	j-invariant
L	3.9312225796235	L(r)(E,1)/r!
Ω	0.9904005044937	Real period
R	1.984663053879	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	29760u1 7440ba1 89280fm1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 29760bt1

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	2	-4	-4	-4	8	-	-2	-6	4	-6	4	6	10	-8	6	10	8	8	12	-18

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Quadratic twists for elliptic curve 29760bt1

-4	8	-3
29760u1	7440ba1	89280fm1

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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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