Cremona's table of elliptic curves

7735 = 5 · 7 · 13 · 17

Field	Data	Notes
Atkin-Lehner	5+ 7+ 13- 17+	Signs for the Atkin-Lehner involutions
Class	7735b	Isogeny class
Conductor	7735	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	8160	Modular degree for the optimal curve
Δ	-2018859171875 = -1 · 56 · 7 · 13 · 175	Discriminant
Eigenvalues	1  1 5+ 7+ -5 13- 17+  1	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,2691,42471]	[a1,a2,a3,a4,a6]
j	2156238418114871/2018859171875	j-invariant
L	1.0848625232419	L(r)(E,1)/r!
Ω	0.54243126162097	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	123760bf1 69615u1 38675l1 54145v1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 7735b1

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
1	1	+	+	-5	-	+	1	0	-4	-2	-3	0	-7	7	-1	4	6	2	-8	14	-8	3	5	0

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Quadratic twists for elliptic curve 7735b1

-4	-3	5	-7	13
123760bf1	69615u1	38675l1	54145v1	100555o1

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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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