Cremona's table of elliptic curves

121275 = 3² · 5² · 7² · 11

Field	Data	Notes
Atkin-Lehner	3+ 5+ 7+ 11-	Signs for the Atkin-Lehner involutions
Class	121275k	Isogeny class
Conductor	121275	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	506880	Modular degree for the optimal curve
Δ	-3064088671875 = -1 · 33 · 58 · 74 · 112	Discriminant
Eigenvalues	2 3+ 5+ 7+ 11- -1  8 -5	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-33075,2316781]	[a1,a2,a3,a4,a6]
j	-3950456832/3025	j-invariant
L	6.3476047991463	L(r)(E,1)/r!
Ω	0.793450727258	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	121275f1 24255d1 121275bi1	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 121275k1

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	+	+	+	-	-1	8	-5	6	0	-3	3	0	7	12	10	14	6	3	-12	11	5	8	-16	2

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Quadratic twists for elliptic curve 121275k1

-3	5	-7
121275f1	24255d1	121275bi1

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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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