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	7735c	Isogeny class
Conductor	7735	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	8192	Modular degree for the optimal curve
Δ	14869570625 = 54 · 72 · 134 · 17	Discriminant
Eigenvalues	-1  0 5+ 7+ -4 13- 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-10903,440862]	[a1,a2,a3,a4,a6]
Generators	[-108:645:1]	Generators of the group modulo torsion
j	143325809988740289/14869570625	j-invariant
L	1.9216295083991	L(r)(E,1)/r!
Ω	1.1957997241453	Real period
R	1.6069827326416	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	123760bh1 69615t1 38675h1 54145s1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 7735c1

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	0	+	+	-4	-	-	4	-4	-2	8	-6	-10	12	0	6	-4	6	12	-8	6	-4	-4	-6	6

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Quadratic twists for elliptic curve 7735c1

-4	-3	5	-7	13
123760bh1	69615t1	38675h1	54145s1	100555q1

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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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