Properties

Label 162240dc
Number of curves $1$
Conductor $162240$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("dc1")
 
E.isogeny_class()
 

Elliptic curves in class 162240dc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162240.dx1 162240dc1 \([0, -1, 0, -128665, -18198233]\) \(-762549907456/24024195\) \(-7421452841200320\) \([]\) \(1128960\) \(1.8216\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 162240dc1 has rank \(1\).

Complex multiplication

The elliptic curves in class 162240dc do not have complex multiplication.

Modular form 162240.2.a.dc

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