Cremona's table of elliptic curves

19680 = 2⁵ · 3 · 5 · 41

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 41+	Signs for the Atkin-Lehner involutions
Class	19680bc	Isogeny class
Conductor	19680	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	11520	Modular degree for the optimal curve
Δ	-21172531200 = -1 · 212 · 3 · 52 · 413	Discriminant
Eigenvalues	2- 3- 5- -2 -3 -2  3  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,435,-5925]	[a1,a2,a3,a4,a6]
j	2217342464/5169075	j-invariant
L	2.5076765244162	L(r)(E,1)/r!
Ω	0.62691913110404	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	19680s1 39360bo1 59040n1 98400c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 19680bc1

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	-3	-2	3	6	4	-5	5	3	+	-9	-3	2	-8	-7	-12	13	7	8	12	6	0

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Quadratic twists for elliptic curve 19680bc1

-4	8	-3	5
19680s1	39360bo1	59040n1	98400c1

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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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