Cremona's table of elliptic curves

781 = 11 · 71

Field	Data	Notes
Atkin-Lehner	11+ 71-	Signs for the Atkin-Lehner involutions
Class	781a	Isogeny class
Conductor	781	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	612	Modular degree for the optimal curve
Δ	167414286061 = 119 · 71	Discriminant
Eigenvalues	0  0 -1 -3 11+  7  3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-1378,347]	[a1,a2,a3,a4,a6]
j	289381900713984/167414286061	j-invariant
L	0.86273730686811	L(r)(E,1)/r!
Ω	0.86273730686811	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	12496h1 49984j1 7029f1 19525a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 781a1

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	+	7	3	-2	8	4	10	1	-11	-2	2	0	4	-11	8	-	16	6	14	-15	-10

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Quadratic twists for elliptic curve 781a1

-4	8	-3	5	-7	-11	-71
12496h1	49984j1	7029f1	19525a1	38269c1	8591a1	55451c1

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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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