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	1278h	Isogeny class
Conductor	1278	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	29399112 = 23 · 36 · 712	Discriminant
Eigenvalues	2- 3- -2  0 -6  4 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-371,2827]	[a1,a2,a3,a4,a6]
Generators	[-7:74:1]	Generators of the group modulo torsion
j	7727161833/40328	j-invariant
L	3.3668133515972	L(r)(E,1)/r!
Ω	2.1062653732642	Real period
R	0.53282512804159	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	10224r2 40896m2 142c2 31950m2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1278h2

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	0	-6	4	-6	-8	4	2	-8	10	2	-8	4	0	-10	-8	2	+	-2	0	4	-6	14

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Quadratic twists for elliptic curve 1278h2

-4	8	-3	5	-7	-71
10224r2	40896m2	142c2	31950m2	62622cd2	90738bb2

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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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