Cremona's table of elliptic curves

1856 = 2⁶ · 29

Field	Data	Notes
Atkin-Lehner	2- 29-	Signs for the Atkin-Lehner involutions
Class	1856p	Isogeny class
Conductor	1856	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	-475136 = -1 · 214 · 29	Discriminant
Eigenvalues	2- -3 -3 -4 -1  3  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-19324,1033936]	[a1,a2,a3,a4,a6]
Generators	[80:4:1]	Generators of the group modulo torsion
j	-48707390098512/29	j-invariant
L	1.2874526337344	L(r)(E,1)/r!
Ω	1.8141240425872	Real period
R	0.35484140100428	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	1856g1 464f1 16704cr1 46400ci1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1856p1

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
-	-3	-3	-4	-1	3	2	4	6	-	-9	8	-8	-5	7	5	-10	-10	8	2	0	1	6	12	0

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Quadratic twists for elliptic curve 1856p1

-4	8	-3	5	-7	29
1856g1	464f1	16704cr1	46400ci1	90944em1	53824bf1

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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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