Cremona's table of elliptic curves

1414 = 2 · 7 · 101

Field	Data	Notes
Atkin-Lehner	2+ 7+ 101+	Signs for the Atkin-Lehner involutions
Class	1414a	Isogeny class
Conductor	1414	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	360	Modular degree for the optimal curve
Δ	-2217152 = -1 · 26 · 73 · 101	Discriminant
Eigenvalues	2+  1  2 7+ -2 -2  0 -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-325,2224]	[a1,a2,a3,a4,a6]
Generators	[11:-2:1]	Generators of the group modulo torsion
j	-3779648905033/2217152	j-invariant
L	2.4759005260778	L(r)(E,1)/r!
Ω	2.5687753473239	Real period
R	0.48192235429561	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	11312k1 45248h1 12726i1 35350p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1414a1

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	-2	0	-8	1	-4	0	-11	2	7	4	-14	-5	7	2	13	11	15	-7	-1	-10

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Quadratic twists for elliptic curve 1414a1

-4	8	-3	5	-7
11312k1	45248h1	12726i1	35350p1	9898b1

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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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