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	1278g	Isogeny class
Conductor	1278	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	288	Modular degree for the optimal curve
Δ	-11179944 = -1 · 23 · 39 · 71	Discriminant
Eigenvalues	2- 3+ -1 -3 -3 -2  6  1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,52,55]	[a1,a2,a3,a4,a6]
Generators	[7:23:1]	Generators of the group modulo torsion
j	804357/568	j-invariant
L	3.3705577839149	L(r)(E,1)/r!
Ω	1.4392285546616	Real period
R	0.39031995914268	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	10224g1 40896h1 1278b1 31950g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1278g1

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	-3	-3	-2	6	1	-4	-5	-11	-2	-5	-11	-4	12	7	1	2	-	1	12	8	6	8

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Quadratic twists for elliptic curve 1278g1

-4	8	-3	5	-7	-71
10224g1	40896h1	1278b1	31950g1	62622bp1	90738s1

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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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