Cremona's table of elliptic curves

1891 = 31 · 61

Field	Data	Notes
Atkin-Lehner	31+ 61+	Signs for the Atkin-Lehner involutions
Class	1891a	Isogeny class
Conductor	1891	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	720	Modular degree for the optimal curve
Δ	-56334781 = -1 · 314 · 61	Discriminant
Eigenvalues	1  2 -3  3 -3  5 -8 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,91,-106]	[a1,a2,a3,a4,a6]
Generators	[202:2782:1]	Generators of the group modulo torsion
j	81916141607/56334781	j-invariant
L	4.2640735103194	L(r)(E,1)/r!
Ω	1.1232626757187	Real period
R	1.8980749572184	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	30256i1 121024f1 17019b1 47275c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1891a1

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	-3	3	-3	5	-8	-4	1	-6	+	8	-11	-8	4	2	3	+	3	-8	-15	5	12	0	2

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Quadratic twists for elliptic curve 1891a1

-4	8	-3	5	-7	-31	61
30256i1	121024f1	17019b1	47275c1	92659h1	58621b1	115351b1

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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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