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	1278i	Isogeny class
Conductor	1278	Conductor
∏ cp	27	Product of Tamagawa factors cp
deg	4536	Modular degree for the optimal curve
Δ	6946975383552 = 227 · 36 · 71	Discriminant
Eigenvalues	2- 3- -2 -3  6 -5 -6  1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-23636,-1386953]	[a1,a2,a3,a4,a6]
Generators	[-91:109:1]	Generators of the group modulo torsion
j	2003092024307193/9529458688	j-invariant
L	3.3059193011094	L(r)(E,1)/r!
Ω	0.38515171493508	Real period
R	0.31790447984188	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	10224s1 40896o1 142e1 31950r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1278i1

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
-	-	-2	-3	6	-5	-6	1	-5	2	-5	-2	-10	1	1	-6	2	-2	2	+	7	-6	4	-9	2

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Quadratic twists for elliptic curve 1278i1

-4	8	-3	5	-7	-71
10224s1	40896o1	142e1	31950r1	62622cc1	90738bc1

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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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