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	29760o	Isogeny class
Conductor	29760	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	55296	Modular degree for the optimal curve
Δ	48758784000 = 222 · 3 · 53 · 31	Discriminant
Eigenvalues	2+ 3+ 5-  4  4 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-15585,754017]	[a1,a2,a3,a4,a6]
j	1597099875769/186000	j-invariant
L	3.257247749173	L(r)(E,1)/r!
Ω	1.085749249724	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	29760cx1 930g1 89280bh1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 29760o1

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

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Quadratic twists for elliptic curve 29760o1

-4	8	-3
29760cx1	930g1	89280bh1

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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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