Cremona's table of elliptic curves

2821 = 7 · 13 · 31

Field	Data	Notes
Atkin-Lehner	7- 13+ 31+	Signs for the Atkin-Lehner involutions
Class	2821b	Isogeny class
Conductor	2821	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	360	Modular degree for the optimal curve
Δ	1796977 = 73 · 132 · 31	Discriminant
Eigenvalues	1  0  0 7-  0 13+  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-217,-1176]	[a1,a2,a3,a4,a6]
j	1132995515625/1796977	j-invariant
L	1.865621238788	L(r)(E,1)/r!
Ω	1.2437474925253	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	45136e1 25389j1 70525g1 19747b1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2821b1

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
1	0	0	-	0	+	2	4	-2	6	+	4	4	10	12	-6	0	2	4	-16	6	-10	4	6	12

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Quadratic twists for elliptic curve 2821b1

-4	-3	5	-7	13	-31
45136e1	25389j1	70525g1	19747b1	36673a1	87451f1

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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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