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	780d	Isogeny class
Conductor	780	Conductor
∏ cp	3	Product of Tamagawa factors cp
Δ	-210912000 = -1 · 28 · 3 · 53 · 133	Discriminant
Eigenvalues	2- 3- 5+ -1  3 13-  3  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-221,-1521]	[a1,a2,a3,a4,a6]
j	-4684079104/823875	j-invariant
L	1.8390125649826	L(r)(E,1)/r!
Ω	0.61300418832752	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3120p2 12480j2 2340i2 3900a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 780d2

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	3	-	3	2	3	6	2	-7	9	8	-6	3	0	-7	-4	3	-10	-1	0	3	-1

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Quadratic twists for elliptic curve 780d2

-4	8	-3	5	-7	-11	13
3120p2	12480j2	2340i2	3900a2	38220l2	94380o2	10140k2

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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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