Cremona's table of elliptic curves

12054 = 2 · 3 · 7² · 41

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7- 41+	Signs for the Atkin-Lehner involutions
Class	12054d	Isogeny class
Conductor	12054	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	131328	Modular degree for the optimal curve
Δ	-15640735740116886 = -1 · 2 · 39 · 78 · 413	Discriminant
Eigenvalues	2+ 3+ -3 7-  0  1  3  1	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-101994,13864194]	[a1,a2,a3,a4,a6]
j	-997392270041497/132944060214	j-invariant
L	0.76092535087499	L(r)(E,1)/r!
Ω	0.38046267543749	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	96432cp1 36162db1 1722g1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 12054d1

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	-	0	1	3	1	6	0	-11	8	+	-10	0	12	15	-8	11	-3	13	8	-9	15	-8

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Quadratic twists for elliptic curve 12054d1

-4	-3	-7
96432cp1	36162db1	1722g1

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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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