Cremona's table of elliptic curves

51984 = 2⁴ · 3² · 19²

Field	Data	Notes
Atkin-Lehner	2- 3+ 19-	Signs for the Atkin-Lehner involutions
Class	51984bn	Isogeny class
Conductor	51984	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	3456	Modular degree for the optimal curve
Δ	-155952 = -1 · 24 · 33 · 192	Discriminant
Eigenvalues	2- 3+  0  1  0  7  0 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,0,19]	[a1,a2,a3,a4,a6]
Generators	[5:12:1]	Generators of the group modulo torsion
j	0	j-invariant
L	7.2150025633068	L(r)(E,1)/r!
Ω	2.5751354345138	Real period
R	1.4008976900076	Regulator
r	1	Rank of the group of rational points
S	0.9999999999962	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	12996e1 51984bn2 51984bd1	Quadratic twists by: -4 -3 -19

Hecke Eigenvalues for elliptic curve 51984bn1

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	1	0	7	0	-	0	0	11	1	0	-5	0	0	0	-13	5	0	-7	-13	0	0	-14

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Quadratic twists for elliptic curve 51984bn1

-4	-3	-19
12996e1	51984bn2	51984bd1

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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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