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	107712ea	Isogeny class
Conductor	107712	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	663552	Modular degree for the optimal curve
Δ	21406095265370112 = 212 · 39 · 11 · 176	Discriminant
Eigenvalues	2- 3- -2  2 11+ -4 17- -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-121476,-14697344]	[a1,a2,a3,a4,a6]
Generators	[-250:216:1] [-214:1224:1]	Generators of the group modulo torsion
j	66390766775488/7168857993	j-invariant
L	10.818171271127	L(r)(E,1)/r!
Ω	0.25751675982204	Real period
R	3.5007984458216	Regulator
r	2	Rank of the group of rational points
S	1.0000000000398	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	107712fe1 53856bd1 35904cx1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 107712ea1

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

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Quadratic twists for elliptic curve 107712ea1

-4	8	-3
107712fe1	53856bd1	35904cx1

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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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