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	13398bf	Isogeny class
Conductor	13398	Conductor
∏ cp	128	Product of Tamagawa factors cp
deg	24576	Modular degree for the optimal curve
Δ	-776390841072 = -1 · 24 · 34 · 7 · 112 · 294	Discriminant
Eigenvalues	2- 3-  2 7+ 11+  2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,308,42368]	[a1,a2,a3,a4,a6]
j	3230633786687/776390841072	j-invariant
L	5.5511281549098	L(r)(E,1)/r!
Ω	0.69389101936372	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	107184bz1 40194m1 93786cb1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 13398bf1

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	6	-4	0	-	4	-10	6	-4	4	-10	8	14	12	0	6	8	16	-2	14

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Quadratic twists for elliptic curve 13398bf1

-4	-3	-7
107184bz1	40194m1	93786cb1

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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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