Properties

Label 128576bm
Number of curves $1$
Conductor $128576$
CM no
Rank $1$

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

Elliptic curves in class 128576bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
128576.ba1 128576bm1 \([0, -1, 0, -99241, -11953423]\) \(373698304/1681\) \(486237075014656\) \([]\) \(548352\) \(1.6698\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 128576bm1 has rank \(1\).

Complex multiplication

The elliptic curves in class 128576bm do not have complex multiplication.

Modular form 128576.2.a.bm

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - 2 q^{9} + 5 q^{11} - 2 q^{13} + q^{15} + 3 q^{17} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display