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	121275f	Isogeny class
Conductor	121275	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1520640	Modular degree for the optimal curve
Δ	-2233720641796875 = -1 · 39 · 58 · 74 · 112	Discriminant
Eigenvalues	-2 3+ 5+ 7+ 11+ -1 -8 -5	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-297675,-62553094]	[a1,a2,a3,a4,a6]
Generators	[645:3712:1]	Generators of the group modulo torsion
j	-3950456832/3025	j-invariant
L	1.9708023610584	L(r)(E,1)/r!
Ω	0.10219132374313	Real period
R	2.4106773331138	Regulator
r	1	Rank of the group of rational points
S	0.99999994862537	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	121275k1 24255n1 121275x1	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 121275f1

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 121275f1

-3	5	-7
121275k1	24255n1	121275x1

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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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