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	1278c	Isogeny class
Conductor	1278	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-7891699181274 = -1 · 2 · 37 · 715	Discriminant
Eigenvalues	2+ 3- -1  3  3 -6  2  5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-2070,140454]	[a1,a2,a3,a4,a6]
j	-1345938541921/10825376106	j-invariant
L	1.2673023741707	L(r)(E,1)/r!
Ω	0.63365118708537	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	10224q2 40896l2 426a2 31950cg2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1278c2

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	-6	2	5	6	-5	7	8	-7	-11	12	6	5	-13	8	+	9	10	6	10	18

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Quadratic twists for elliptic curve 1278c2

-4	8	-3	5	-7	-71
10224q2	40896l2	426a2	31950cg2	62622p2	90738l2

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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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