Cremona's table of elliptic curves

21312 = 2⁶ · 3² · 37

Field	Data	Notes
Atkin-Lehner	2- 3+ 37-	Signs for the Atkin-Lehner involutions
Class	21312bn	Isogeny class
Conductor	21312	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	8192	Modular degree for the optimal curve
Δ	-261881856 = -1 · 218 · 33 · 37	Discriminant
Eigenvalues	2- 3+ -2  4 -4  2  6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,84,720]	[a1,a2,a3,a4,a6]
Generators	[-3:21:1]	Generators of the group modulo torsion
j	9261/37	j-invariant
L	5.2023862987602	L(r)(E,1)/r!
Ω	1.2451545654316	Real period
R	2.0890524129255	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	21312h1 5328i1 21312bj1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 21312bn1

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

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Quadratic twists for elliptic curve 21312bn1

-4	8	-3
21312h1	5328i1	21312bj1

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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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