Cremona's table of elliptic curves

780 = 2² · 3 · 5 · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 13+	Signs for the Atkin-Lehner involutions
Class	780c	Isogeny class
Conductor	780	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	34117200 = 24 · 38 · 52 · 13	Discriminant
Eigenvalues	2- 3- 5+ -2 -6 13+ -2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-81,0]	[a1,a2,a3,a4,a6]
Generators	[-3:15:1]	Generators of the group modulo torsion
j	3718856704/2132325	j-invariant
L	2.3706082460728	L(r)(E,1)/r!
Ω	1.7695272041172	Real period
R	0.1116403786916	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	3120n1 12480r1 2340h1 3900d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 780c1

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
-	-	+	-2	-6	+	-2	-2	-4	2	-2	2	-6	0	6	-2	-6	14	2	-10	-6	4	2	-14	18

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Quadratic twists for elliptic curve 780c1

-4	8	-3	5	-7	-11	13
3120n1	12480r1	2340h1	3900d1	38220q1	94380s1	10140l1

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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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