Cremona's table of elliptic curves

874 = 2 · 19 · 23

Field	Data	Notes
Atkin-Lehner	2- 19+ 23-	Signs for the Atkin-Lehner involutions
Class	874d	Isogeny class
Conductor	874	Conductor
∏ cp	5	Product of Tamagawa factors cp
deg	80	Modular degree for the optimal curve
Δ	13984 = 25 · 19 · 23	Discriminant
Eigenvalues	2-  1 -3 -2 -5  2 -4 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-12,-16]	[a1,a2,a3,a4,a6]
Generators	[-2:2:1]	Generators of the group modulo torsion
j	192100033/13984	j-invariant
L	3.1207398501935	L(r)(E,1)/r!
Ω	2.5757683246946	Real period
R	0.24231525951105	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	6992p1 27968r1 7866g1 21850b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 874d1

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	-2	-5	2	-4	+	-	-3	8	-4	2	5	-13	8	1	-2	8	0	11	-15	-9	3	-1

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Quadratic twists for elliptic curve 874d1

-4	8	-3	5	-7	-11	-19	-23
6992p1	27968r1	7866g1	21850b1	42826u1	105754j1	16606i1	20102q1

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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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