Cremona's table of elliptic curves

1780 = 2² · 5 · 89

Field	Data	Notes
Atkin-Lehner	2- 5+ 89-	Signs for the Atkin-Lehner involutions
Class	1780b	Isogeny class
Conductor	1780	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	1248	Modular degree for the optimal curve
Δ	633680 = 24 · 5 · 892	Discriminant
Eigenvalues	2-  2 5+ -2  0 -6  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-13201,-579414]	[a1,a2,a3,a4,a6]
Generators	[6645:89623:27]	Generators of the group modulo torsion
j	15902196690141184/39605	j-invariant
L	3.4969115761513	L(r)(E,1)/r!
Ω	0.44539476219675	Real period
R	5.2341755718066	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	7120k1 28480w1 16020c1 8900c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1780b1

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

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Quadratic twists for elliptic curve 1780b1

-4	8	-3	5	-7
7120k1	28480w1	16020c1	8900c1	87220o1

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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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