Cremona's table of elliptic curves

1891 = 31 · 61

Field	Data	Notes
Atkin-Lehner	31+ 61+	Signs for the Atkin-Lehner involutions
Class	1891b	Isogeny class
Conductor	1891	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	4480	Modular degree for the optimal curve
Δ	-56334781 = -1 · 314 · 61	Discriminant
Eigenvalues	-1  2 -3 -3  3  5 -4  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-51832,-4563578]	[a1,a2,a3,a4,a6]
Generators	[802:21290:1]	Generators of the group modulo torsion
j	-15399908364408365953/56334781	j-invariant
L	2.1640303917981	L(r)(E,1)/r!
Ω	0.15820493387523	Real period
R	6.8393264950408	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	30256h1 121024g1 17019a1 47275a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1891b1

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	-4	8	-1	-6	+	-4	5	-8	8	-2	-3	+	-3	-16	9	-13	0	-12	2

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Quadratic twists for elliptic curve 1891b1

-4	8	-3	5	-7	-31	61
30256h1	121024g1	17019a1	47275a1	92659j1	58621e1	115351a1

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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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