Cremona's table of elliptic curves

1978 = 2 · 23 · 43

Field	Data	Notes
Atkin-Lehner	2- 23+ 43-	Signs for the Atkin-Lehner involutions
Class	1978d	Isogeny class
Conductor	1978	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	80	Modular degree for the optimal curve
Δ	-3956 = -1 · 22 · 23 · 43	Discriminant
Eigenvalues	2-  1 -2  0 -3 -1  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-4,4]	[a1,a2,a3,a4,a6]
Generators	[0:2:1]	Generators of the group modulo torsion
j	-7189057/3956	j-invariant
L	4.3332389270289	L(r)(E,1)/r!
Ω	4.0903913126993	Real period
R	0.52968513227275	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	15824j1 63296e1 17802i1 49450g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1978d1

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	0	-3	-1	2	-4	+	-6	4	1	-6	-	-2	4	-8	-1	3	-13	8	-7	15	5	-8

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Quadratic twists for elliptic curve 1978d1

-4	8	-3	5	-7	-23	-43
15824j1	63296e1	17802i1	49450g1	96922r1	45494j1	85054a1

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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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