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	1254h	Isogeny class
Conductor	1254	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	761097744 = 24 · 32 · 114 · 192	Discriminant
Eigenvalues	2- 3+ -2  0 11- -2 -6 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-229,-229]	[a1,a2,a3,a4,a6]
Generators	[-3:22:1]	Generators of the group modulo torsion
j	1328460616657/761097744	j-invariant
L	2.9949273771176	L(r)(E,1)/r!
Ω	1.3311379590426	Real period
R	2.2499000624036	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	8	Number of elements in the torsion subgroup
Twists	10032o2 40128t2 3762d2 31350t2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1254h2

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	-	-2	-6	+	0	-2	0	-2	-6	4	-8	6	-12	-2	-4	-16	10	0	-12	10	2

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Quadratic twists for elliptic curve 1254h2

-4	8	-3	5	-7	-11	-19
10032o2	40128t2	3762d2	31350t2	61446dg2	13794i2	23826u2

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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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