Properties

Label 23232cm
Number of curves $1$
Conductor $23232$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("cm1")
 
E.isogeny_class()
 

Elliptic curves in class 23232cm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23232.ca1 23232cm1 \([0, 1, 0, 15, 9]\) \(45056/27\) \(-209088\) \([]\) \(2880\) \(-0.28984\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 23232cm1 has rank \(1\).

Complex multiplication

The elliptic curves in class 23232cm do not have complex multiplication.

Modular form 23232.2.a.cm

sage: E.q_eigenform(10)
 
\(q + q^{3} - 4 q^{5} - q^{7} + q^{9} - 2 q^{13} - 4 q^{15} - 4 q^{17} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display