Cremona's table of elliptic curves

10656 = 2⁵ · 3² · 37

Field	Data	Notes
Atkin-Lehner	2- 3- 37+	Signs for the Atkin-Lehner involutions
Class	10656r	Isogeny class
Conductor	10656	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	8064	Modular degree for the optimal curve
Δ	110481408 = 212 · 36 · 37	Discriminant
Eigenvalues	2- 3-  4 -1 -3  2 -8 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2088,-36720]	[a1,a2,a3,a4,a6]
Generators	[-3280:172:125]	Generators of the group modulo torsion
j	337153536/37	j-invariant
L	5.5506587010919	L(r)(E,1)/r!
Ω	0.706268425249	Real period
R	3.9295673589931	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	10656f1 21312bb1 1184d1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 10656r1

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	-1	-3	2	-8	-2	6	0	-8	+	5	-2	-11	-9	6	-6	4	-5	11	8	-5	18	-2

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Quadratic twists for elliptic curve 10656r1

-4	8	-3
10656f1	21312bb1	1184d1

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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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