Cremona's table of elliptic curves

2121 = 3 · 7 · 101

Field	Data	Notes
Atkin-Lehner	3+ 7- 101-	Signs for the Atkin-Lehner involutions
Class	2121b	Isogeny class
Conductor	2121	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	320	Modular degree for the optimal curve
Δ	2182509 = 32 · 74 · 101	Discriminant
Eigenvalues	0 3+  1 7- -6  1  5 -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-35,50]	[a1,a2,a3,a4,a6]
Generators	[-4:10:1]	Generators of the group modulo torsion
j	4878401536/2182509	j-invariant
L	2.3363801751581	L(r)(E,1)/r!
Ω	2.3373799540477	Real period
R	0.12494653314238	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	33936e1 6363c1 53025l1 14847e1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2121b1

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	-	-6	1	5	-1	3	6	-5	-6	-10	12	-3	0	-6	10	-10	7	-16	-1	-6	8	-2

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Quadratic twists for elliptic curve 2121b1

-4	-3	5	-7
33936e1	6363c1	53025l1	14847e1

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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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