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	107712ew	Isogeny class
Conductor	107712	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	1720320	Modular degree for the optimal curve
Δ	28401389862912 = 216 · 36 · 112 · 173	Discriminant
Eigenvalues	2- 3-  0  2 11- -6 17-  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-7133580,-7333468272]	[a1,a2,a3,a4,a6]
Generators	[83586:8231553:8]	Generators of the group modulo torsion
j	840308702533978500/594473	j-invariant
L	7.3072916297137	L(r)(E,1)/r!
Ω	0.092378875347146	Real period
R	6.591777234627	Regulator
r	1	Rank of the group of rational points
S	1.0000000027409	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	107712bg1 26928k1 11968m1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 107712ew1

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

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Quadratic twists for elliptic curve 107712ew1

-4	8	-3
107712bg1	26928k1	11968m1

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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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