Cremona's table of elliptic curves

4697 = 7 · 11 · 61

Field	Data	Notes
Atkin-Lehner	7- 11+ 61-	Signs for the Atkin-Lehner involutions
Class	4697b	Isogeny class
Conductor	4697	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1920	Modular degree for the optimal curve
Δ	-98275331 = -1 · 74 · 11 · 612	Discriminant
Eigenvalues	2 -1  1 7- 11+  2  2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-560,-4941]	[a1,a2,a3,a4,a6]
Generators	[234:423:8]	Generators of the group modulo torsion
j	-19456426971136/98275331	j-invariant
L	6.3692379475625	L(r)(E,1)/r!
Ω	0.49048614553158	Real period
R	1.6231951721744	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	75152i1 42273h1 117425b1 32879a1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4697b1

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	-1	1	-	+	2	2	-2	-7	6	-3	-3	0	-10	-8	6	-9	-	-5	15	6	4	-4	-15	1

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Quadratic twists for elliptic curve 4697b1

-4	-3	5	-7	-11
75152i1	42273h1	117425b1	32879a1	51667d1

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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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