Cremona's table of elliptic curves

11616 = 2⁵ · 3 · 11²

Field	Data	Notes
Atkin-Lehner	2+ 3+ 11+	Signs for the Atkin-Lehner involutions
Class	11616a	Isogeny class
Conductor	11616	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	255552 = 26 · 3 · 113	Discriminant
Eigenvalues	2+ 3+  0  4 11+ -2  2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-18,24]	[a1,a2,a3,a4,a6]
Generators	[-4:4:1]	Generators of the group modulo torsion
j	8000/3	j-invariant
L	4.4444866436163	L(r)(E,1)/r!
Ω	2.8414502665644	Real period
R	1.5641613354684	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	11616x1 23232bh1 34848bq1 11616p1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 11616a1

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	4	+	-2	2	-2	-6	2	8	-2	6	-2	-6	4	-4	-10	-12	-10	-12	8	8	2	-10

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Quadratic twists for elliptic curve 11616a1

-4	8	-3	-11
11616x1	23232bh1	34848bq1	11616p1

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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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