Cremona's table of elliptic curves

781 = 11 · 71

Field	Data	Notes
Atkin-Lehner	11- 71-	Signs for the Atkin-Lehner involutions
Class	781b	Isogeny class
Conductor	781	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	108	Modular degree for the optimal curve
Δ	94501 = 113 · 71	Discriminant
Eigenvalues	0  0 -1  3 11-  1 -3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-808,8840]	[a1,a2,a3,a4,a6]
Generators	[14:16:1]	Generators of the group modulo torsion
j	58338840674304/94501	j-invariant
L	1.9767169680723	L(r)(E,1)/r!
Ω	2.8846769626428	Real period
R	0.22841575141933	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	12496d1 49984e1 7029a1 19525e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 781b1

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

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Quadratic twists for elliptic curve 781b1

-4	8	-3	5	-7	-11	-71
12496d1	49984e1	7029a1	19525e1	38269e1	8591b1	55451a1

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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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