Properties

Label 277725.cl
Number of curves $1$
Conductor $277725$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("cl1")
 
E.isogeny_class()
 

Elliptic curves in class 277725.cl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
277725.cl1 277725cl1 \([1, 1, 0, 12629600, -134699271875]\) \(182074754111/6511640625\) \(-7967703017805260009765625\) \([]\) \(55641600\) \(3.4580\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 277725.cl1 has rank \(1\).

Complex multiplication

The elliptic curves in class 277725.cl do not have complex multiplication.

Modular form 277725.2.a.cl

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} - q^{4} - q^{6} + q^{7} - 3 q^{8} + q^{9} + 5 q^{11} + q^{12} - q^{13} + q^{14} - q^{16} + q^{18} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display