Properties

Label 277725bm
Number of curves $1$
Conductor $277725$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bm1")
 
E.isogeny_class()
 

Elliptic curves in class 277725bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
277725.bm1 277725bm1 \([0, -1, 1, -811133, 318654293]\) \(-48234496/7875\) \(-9635922016998046875\) \([]\) \(5087232\) \(2.3702\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 277725bm1 has rank \(1\).

Complex multiplication

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

Modular form 277725.2.a.bm

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{4} + q^{7} + q^{9} + 4 q^{11} + 2 q^{12} - 3 q^{13} + 4 q^{16} + q^{17} + O(q^{20})\) Copy content Toggle raw display