Cremona's table of elliptic curves

20672 = 2⁶ · 17 · 19

Field	Data	Notes
Atkin-Lehner	2+ 17+ 19+	Signs for the Atkin-Lehner involutions
Class	20672b	Isogeny class
Conductor	20672	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2048	Modular degree for the optimal curve
Δ	351424 = 26 · 172 · 19	Discriminant
Eigenvalues	2+  0 -2 -2  2 -6 17+ 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-31,60]	[a1,a2,a3,a4,a6]
Generators	[8:18:1]	Generators of the group modulo torsion
j	51478848/5491	j-invariant
L	3.1521787125328	L(r)(E,1)/r!
Ω	2.9377682119459	Real period
R	2.1459682896118	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	20672g1 10336b2	Quadratic twists by: -4 8

Hecke Eigenvalues for elliptic curve 20672b1

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	2	-6	+	+	6	0	4	-8	0	4	8	-6	12	6	12	-12	14	8	16	-2	8

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Quadratic twists for elliptic curve 20672b1

-4	8
20672g1	10336b2

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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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