Cremona's table of elliptic curves

1278 = 2 · 3² · 71

Field	Data	Notes
Atkin-Lehner	2+ 3- 71+	Signs for the Atkin-Lehner involutions
Class	1278d	Isogeny class
Conductor	1278	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	504	Modular degree for the optimal curve
Δ	26500608 = 29 · 36 · 71	Discriminant
Eigenvalues	2+ 3-  4 -3  0  1  0 -5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-105,-307]	[a1,a2,a3,a4,a6]
j	176558481/36352	j-invariant
L	1.5123519271339	L(r)(E,1)/r!
Ω	1.5123519271339	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	10224t1 40896t1 142a1 31950ce1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1278d1

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
+	-	4	-3	0	1	0	-5	7	8	7	4	-4	-5	13	6	-10	-2	-4	+	7	0	4	3	-4

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Quadratic twists for elliptic curve 1278d1

-4	8	-3	5	-7	-71
10224t1	40896t1	142a1	31950ce1	62622r1	90738q1

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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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