Cremona's table of elliptic curves

765 = 3² · 5 · 17

Field	Data	Notes
Atkin-Lehner	3- 5- 17+	Signs for the Atkin-Lehner involutions
Class	765c	Isogeny class
Conductor	765	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-131675625 = -1 · 36 · 54 · 172	Discriminant
Eigenvalues	-1 3- 5- -2 -2  2 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-32,564]	[a1,a2,a3,a4,a6]
Generators	[2:21:1]	Generators of the group modulo torsion
j	-4826809/180625	j-invariant
L	1.5493056096194	L(r)(E,1)/r!
Ω	1.5391747803274	Real period
R	0.25164549689573	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	12240bx2 48960bp2 85a2 3825h2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 765c2

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	+	0	-6	6	-10	2	-10	4	-12	10	-8	-14	8	2	-14	-14	-4	-6	2

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Quadratic twists for elliptic curve 765c2

-4	8	-3	5	-7	-11	13	17
12240bx2	48960bp2	85a2	3825h2	37485bd2	92565bw2	129285q2	13005i2

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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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