Cremona's table of elliptic curves

11712 = 2⁶ · 3 · 61

Field	Data	Notes
Atkin-Lehner	2+ 3+ 61+	Signs for the Atkin-Lehner involutions
Class	11712b	Isogeny class
Conductor	11712	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-1328435116376064 = -1 · 219 · 3 · 615	Discriminant
Eigenvalues	2+ 3+ -1 -2 -2 -4 -7  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-32961,-2883903]	[a1,a2,a3,a4,a6]
Generators	[401:6944:1]	Generators of the group modulo torsion
j	-15107691357361/5067577806	j-invariant
L	2.7753936933026	L(r)(E,1)/r!
Ω	0.17420099071269	Real period
R	3.9830337387117	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	11712be2 366b2 35136j2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 11712b2

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
+	+	-1	-2	-2	-4	-7	0	9	10	-8	7	12	1	8	6	0	+	12	-3	-1	10	1	5	-17

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Quadratic twists for elliptic curve 11712b2

-4	8	-3
11712be2	366b2	35136j2

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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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