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	4	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	309825 = 36 · 52 · 17	Discriminant
Eigenvalues	-1 3- 5- -2 -2  2 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-77,276]	[a1,a2,a3,a4,a6]
Generators	[-4:24:1]	Generators of the group modulo torsion
j	68417929/425	j-invariant
L	1.5493056096194	L(r)(E,1)/r!
Ω	3.0783495606548	Real period
R	0.50329099379145	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	12240bx1 48960bp1 85a1 3825h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 765c1

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 765c1

-4	8	-3	5	-7	-11	13	17
12240bx1	48960bp1	85a1	3825h1	37485bd1	92565bw1	129285q1	13005i1

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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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