Properties

Label 139650.cm
Number of curves $1$
Conductor $139650$
CM no
Rank $1$

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

Elliptic curves in class 139650.cm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139650.cm1 139650fi1 \([1, 0, 1, -593171, 1128294038]\) \(-1569510182075597/36491419872936\) \(-536647382078880933000\) \([]\) \(7354368\) \(2.6584\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 139650.cm1 has rank \(1\).

Complex multiplication

The elliptic curves in class 139650.cm do not have complex multiplication.

Modular form 139650.2.a.cm

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} - 5 q^{11} + q^{12} - q^{13} + q^{16} - 3 q^{17} - q^{18} + q^{19} + O(q^{20})\)  Toggle raw display