Cremona's table of elliptic curves

2314 = 2 · 13 · 89

Field	Data	Notes
Atkin-Lehner	2+ 13- 89+	Signs for the Atkin-Lehner involutions
Class	2314a	Isogeny class
Conductor	2314	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	832	Modular degree for the optimal curve
Δ	-60164 = -1 · 22 · 132 · 89	Discriminant
Eigenvalues	2+  3  3  0 -2 13-  7  5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-73,-223]	[a1,a2,a3,a4,a6]
j	-43354526697/60164	j-invariant
L	3.2642558656122	L(r)(E,1)/r!
Ω	0.81606396640304	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	18512j1 74048b1 20826bh1 57850q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2314a1

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
+	3	3	0	-2	-	7	5	-3	-10	-1	-4	12	-11	0	-13	12	-2	2	-4	1	4	12	+	-5

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Quadratic twists for elliptic curve 2314a1

-4	8	-3	5	-7	13
18512j1	74048b1	20826bh1	57850q1	113386h1	30082k1

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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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