Cremona's table of elliptic curves

1254 = 2 · 3 · 11 · 19

Field	Data	Notes
Atkin-Lehner	2+ 3+ 11- 19-	Signs for the Atkin-Lehner involutions
Class	1254c	Isogeny class
Conductor	1254	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-123297834528 = -1 · 25 · 36 · 114 · 192	Discriminant
Eigenvalues	2+ 3+ -4  0 11-  4 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1122,21780]	[a1,a2,a3,a4,a6]
Generators	[11:99:1]	Generators of the group modulo torsion
j	-156425280396841/123297834528	j-invariant
L	1.4099347712638	L(r)(E,1)/r!
Ω	0.95963566098967	Real period
R	0.36730991473621	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	10032n2 40128s2 3762o2 31350cg2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1254c2

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	0	-	4	-2	-	2	2	-2	0	-6	-4	6	-2	-12	-6	0	4	6	-10	-8	-10	14

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Quadratic twists for elliptic curve 1254c2

-4	8	-3	5	-7	-11	-19
10032n2	40128s2	3762o2	31350cg2	61446be2	13794be2	23826bn2

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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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