Cremona's table of elliptic curves

21216 = 2⁵ · 3 · 13 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 13- 17-	Signs for the Atkin-Lehner involutions
Class	21216h	Isogeny class
Conductor	21216	Conductor
∏ cp	144	Product of Tamagawa factors cp
deg	64512	Modular degree for the optimal curve
Δ	8561172439872 = 26 · 36 · 133 · 174	Discriminant
Eigenvalues	2+ 3- -4 -2 -4 13- 17- -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-5530,-74236]	[a1,a2,a3,a4,a6]
Generators	[-58:234:1] [-16:102:1]	Generators of the group modulo torsion
j	292279034436544/133768319373	j-invariant
L	6.8843399481931	L(r)(E,1)/r!
Ω	0.57821924916975	Real period
R	0.33072517994204	Regulator
r	2	Rank of the group of rational points
S	0.99999999999984	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	21216d1 42432bq2 63648v1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 21216h1

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

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Quadratic twists for elliptic curve 21216h1

-4	8	-3
21216d1	42432bq2	63648v1

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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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