Properties

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

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 54450w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54450.i1 54450w1 \([1, -1, 0, -40148367, 96404722541]\) \(7177599/128\) \(127631582105370750000000\) \([]\) \(10644480\) \(3.2295\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 54450w1 has rank \(1\).

Complex multiplication

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

Modular form 54450.2.a.w

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 3 q^{7} - q^{8} - 7 q^{13} + 3 q^{14} + q^{16} - 3 q^{17} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display