Cremona's table of elliptic curves

11248 = 2⁴ · 19 · 37

Field	Data	Notes
Atkin-Lehner	2- 19+ 37-	Signs for the Atkin-Lehner involutions
Class	11248h	Isogeny class
Conductor	11248	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2240	Modular degree for the optimal curve
Δ	-106541056 = -1 · 212 · 19 · 372	Discriminant
Eigenvalues	2-  0 -3 -3  1  2  3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,16,496]	[a1,a2,a3,a4,a6]
Generators	[9:37:1]	Generators of the group modulo torsion
j	110592/26011	j-invariant
L	2.8720515063098	L(r)(E,1)/r!
Ω	1.455754754449	Real period
R	0.98644757900754	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	703b1 44992bc1 101232be1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 11248h1

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	-3	-3	1	2	3	+	0	-4	0	-	-6	3	11	-2	6	5	-6	10	-11	14	12	4	-14

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Quadratic twists for elliptic curve 11248h1

-4	8	-3
703b1	44992bc1	101232be1

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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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