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	121275cr	Isogeny class
Conductor	121275	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	165888	Modular degree for the optimal curve
Δ	-902513390625 = -1 · 37 · 56 · 74 · 11	Discriminant
Eigenvalues	1 3- 5+ 7+ 11- -4  3  1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-5742,175041]	[a1,a2,a3,a4,a6]
Generators	[24:213:1]	Generators of the group modulo torsion
j	-765625/33	j-invariant
L	7.2892257695015	L(r)(E,1)/r!
Ω	0.87791692984347	Real period
R	1.0378581304692	Regulator
r	1	Rank of the group of rational points
S	0.99999999744621	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	40425bt1 4851h1 121275eg1	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 121275cr1

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
1	-	+	+	-	-4	3	1	-1	5	-10	11	-10	3	-9	-8	9	-2	-4	7	-4	-8	8	0	1

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Quadratic twists for elliptic curve 121275cr1

-3	5	-7
40425bt1	4851h1	121275eg1

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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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