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	7735d	Isogeny class
Conductor	7735	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	-10806834390625 = -1 · 56 · 72 · 132 · 174	Discriminant
Eigenvalues	1 -2 5- 7+ -2 13- 17+ -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-9523,-391869]	[a1,a2,a3,a4,a6]
Generators	[195:2177:1]	Generators of the group modulo torsion
j	-95494752302662441/10806834390625	j-invariant
L	3.2559585768035	L(r)(E,1)/r!
Ω	0.24011746933997	Real period
R	1.1299880935199	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	123760bt2 69615k2 38675m2 54145k2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 7735d2

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

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Quadratic twists for elliptic curve 7735d2

-4	-3	5	-7	13
123760bt2	69615k2	38675m2	54145k2	100555i2

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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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