Properties

Label 81120.k
Number of curves $1$
Conductor $81120$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 81120.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
81120.k1 81120a1 \([0, -1, 0, -21181, 1226965]\) \(-53157376/1755\) \(-34697419960320\) \([]\) \(193536\) \(1.3729\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 81120.k1 has rank \(1\).

Complex multiplication

The elliptic curves in class 81120.k do not have complex multiplication.

Modular form 81120.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{7} + q^{9} + q^{11} + q^{15} - 5 q^{17} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display