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
Δ	-3912040797608125 = -1 · 54 · 78 · 13 · 174	Discriminant
Eigenvalues	-1  0 5+ 7+ -4 13- 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,28877,2335456]	[a1,a2,a3,a4,a6]
Generators	[-65:457:1]	Generators of the group modulo torsion
j	2663140198900085631/3912040797608125	j-invariant
L	1.9216295083991	L(r)(E,1)/r!
Ω	0.29894993103632	Real period
R	1.6069827326416	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	123760bh3 69615t3 38675h3 54145s3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 7735c4

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 7735c4

-4	-3	5	-7	13
123760bh3	69615t3	38675h3	54145s3	100555q3

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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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