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	1254b	Isogeny class
Conductor	1254	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	120	Modular degree for the optimal curve
Δ	-20064 = -1 · 25 · 3 · 11 · 19	Discriminant
Eigenvalues	2+ 3+  3  2 11+  0  7 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-6,-12]	[a1,a2,a3,a4,a6]
j	-30664297/20064	j-invariant
L	1.4511965679791	L(r)(E,1)/r!
Ω	1.4511965679791	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	10032r1 40128bb1 3762r1 31350bx1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1254b1

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
+	+	3	2	+	0	7	-	4	1	-2	-3	-2	-5	-8	6	0	13	-1	8	-4	-8	10	-1	8

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Quadratic twists for elliptic curve 1254b1

-4	8	-3	5	-7	-11	-19
10032r1	40128bb1	3762r1	31350bx1	61446z1	13794bc1	23826bg1

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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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