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	13398bh	Isogeny class
Conductor	13398	Conductor
∏ cp	576	Product of Tamagawa factors cp
Δ	12632535839734272 = 29 · 34 · 72 · 118 · 29	Discriminant
Eigenvalues	2- 3-  0 7+ 11- -4 -4  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-59973,1642689]	[a1,a2,a3,a4,a6]
Generators	[-30:1863:1]	Generators of the group modulo torsion
j	23855662743324252625/12632535839734272	j-invariant
L	8.1556575862798	L(r)(E,1)/r!
Ω	0.35047056925799	Real period
R	0.16160133256194	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	107184bv2 40194i2 93786cg2	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 13398bh2

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
-	-	0	+	-	-4	-4	0	0	-	10	-6	0	-4	-2	2	14	-10	-8	0	-4	8	-6	0	-8

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Quadratic twists for elliptic curve 13398bh2

-4	-3	-7
107184bv2	40194i2	93786cg2

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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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