Cremona's table of elliptic curves

20874 = 2 · 3 · 7² · 71

Field	Data	Notes
Atkin-Lehner	2+ 3- 7- 71+	Signs for the Atkin-Lehner involutions
Class	20874o	Isogeny class
Conductor	20874	Conductor
∏ cp	64	Product of Tamagawa factors cp
deg	18432	Modular degree for the optimal curve
Δ	-45377529372 = -1 · 22 · 38 · 73 · 712	Discriminant
Eigenvalues	2+ 3-  2 7-  4 -4 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,625,-8242]	[a1,a2,a3,a4,a6]
Generators	[18:85:1]	Generators of the group modulo torsion
j	78898389569/132296004	j-invariant
L	5.5489196454932	L(r)(E,1)/r!
Ω	0.5978409206812	Real period
R	0.58009993268471	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	62622cq1 20874f1	Quadratic twists by: -3 -7

Hecke Eigenvalues for elliptic curve 20874o1

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

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Quadratic twists for elliptic curve 20874o1

-3	-7
62622cq1	20874f1

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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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