Cremona's table of elliptic curves

6097 = 7 · 13 · 67

Field	Data	Notes
Atkin-Lehner	7+ 13- 67+	Signs for the Atkin-Lehner involutions
Class	6097a	Isogeny class
Conductor	6097	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	4272	Modular degree for the optimal curve
Δ	-69036331 = -1 · 7 · 133 · 672	Discriminant
Eigenvalues	-2 -2 -3 7+  0 13- -8 -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-722,7242]	[a1,a2,a3,a4,a6]
Generators	[16:-7:1] [10:33:1]	Generators of the group modulo torsion
j	-41680861032448/69036331	j-invariant
L	1.7611280822189	L(r)(E,1)/r!
Ω	1.9509241440035	Real period
R	0.15045246527824	Regulator
r	2	Rank of the group of rational points
S	1.0000000000011	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	97552l1 54873k1 42679a1 79261g1	Quadratic twists by: -4 -3 -7 13

Hecke Eigenvalues for elliptic curve 6097a1

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	-3	+	0	-	-8	-1	3	3	-7	0	-6	-11	1	9	4	0	+	0	-11	-7	1	-3	7

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Quadratic twists for elliptic curve 6097a1

-4	-3	-7	13
97552l1	54873k1	42679a1	79261g1

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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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