Cremona's table of elliptic curves

107712 = 2⁶ · 3² · 11 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 11+ 17+	Signs for the Atkin-Lehner involutions
Class	107712dn	Isogeny class
Conductor	107712	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	65536	Modular degree for the optimal curve
Δ	-128592940608 = -1 · 26 · 37 · 11 · 174	Discriminant
Eigenvalues	2- 3- -2  0 11+ -2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-471,-17696]	[a1,a2,a3,a4,a6]
Generators	[132:1490:1]	Generators of the group modulo torsion
j	-247673152/2756193	j-invariant
L	4.4414074215301	L(r)(E,1)/r!
Ω	0.44320023441464	Real period
R	5.0106104164515	Regulator
r	1	Rank of the group of rational points
S	0.99999999983488	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	107712ep1 53856m2 35904dc1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 107712dn1

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	0	+	-2	+	-4	0	-2	4	-6	-2	12	8	-6	12	2	0	0	-10	0	16	-2	-14

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Quadratic twists for elliptic curve 107712dn1

-4	8	-3
107712ep1	53856m2	35904dc1

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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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