Cremona's table of elliptic curves

13398 = 2 · 3 · 7 · 11 · 29

Field	Data	Notes
Atkin-Lehner	2+ 3- 7- 11+ 29+	Signs for the Atkin-Lehner involutions
Class	13398r	Isogeny class
Conductor	13398	Conductor
∏ cp	56	Product of Tamagawa factors cp
Δ	69379682071392 = 25 · 314 · 72 · 11 · 292	Discriminant
Eigenvalues	2+ 3- -2 7- 11+ -2 -4  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-11127,-209414]	[a1,a2,a3,a4,a6]
Generators	[-82:432:1]	Generators of the group modulo torsion
j	152335761701447017/69379682071392	j-invariant
L	3.5517689451192	L(r)(E,1)/r!
Ω	0.48531169563974	Real period
R	0.52275225195182	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	107184bn2 40194ca2 93786e2	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 13398r2

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
+	-	-2	-	+	-2	-4	4	-6	+	4	4	4	10	2	-12	12	2	12	-10	6	-4	0	18	-2

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Quadratic twists for elliptic curve 13398r2

-4	-3	-7
107184bn2	40194ca2	93786e2

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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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