Properties

Label 177600cm
Number of curves $1$
Conductor $177600$
CM no
Rank $2$

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

Elliptic curves in class 177600cm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
177600.bd1 177600cm1 \([0, -1, 0, -16208, 799662]\) \(-18836438080/333\) \(-8325000000\) \([]\) \(268800\) \(1.0312\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 177600cm1 has rank \(2\).

Complex multiplication

The elliptic curves in class 177600cm do not have complex multiplication.

Modular form 177600.2.a.cm

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{7} + q^{9} - 4 q^{11} - 6 q^{13} - 6 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display