Cremona's table of elliptic curves

11312 = 2⁴ · 7 · 101

Field	Data	Notes
Atkin-Lehner	2+ 7+ 101+	Signs for the Atkin-Lehner involutions
Class	11312b	Isogeny class
Conductor	11312	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1344	Modular degree for the optimal curve
Δ	-8868608 = -1 · 28 · 73 · 101	Discriminant
Eigenvalues	2+  1  0 7+  2  6  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-28,-164]	[a1,a2,a3,a4,a6]
Generators	[30:164:1]	Generators of the group modulo torsion
j	-9826000/34643	j-invariant
L	5.3896900402712	L(r)(E,1)/r!
Ω	0.94961953467895	Real period
R	2.8378154847528	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	5656g1 45248y1 101808h1 79184k1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 11312b1

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	0	+	2	6	0	-2	3	-8	-6	-5	2	11	-2	4	-1	-3	-10	-5	7	5	-3	-5	-8

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Quadratic twists for elliptic curve 11312b1

-4	8	-3	-7
5656g1	45248y1	101808h1	79184k1

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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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