Properties

Label 54450by
Number of curves $1$
Conductor $54450$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("by1")
 
E.isogeny_class()
 

Elliptic curves in class 54450by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54450.bd1 54450by1 \([1, -1, 0, -354492, 613726416]\) \(-390625/12672\) \(-159819161163750000000\) \([]\) \(1612800\) \(2.5571\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 54450by1 has rank \(1\).

Complex multiplication

The elliptic curves in class 54450by do not have complex multiplication.

Modular form 54450.2.a.by

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 2 q^{7} - q^{8} - q^{13} + 2 q^{14} + q^{16} + 4 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display