Properties

Label 54390.bc
Number of curves $1$
Conductor $54390$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bc1")
 
E.isogeny_class()
 

Elliptic curves in class 54390.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54390.bc1 54390bh1 \([1, 0, 1, -2623, 50978]\) \(40708441207609/449550000\) \(22027950000\) \([]\) \(57600\) \(0.79912\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 54390.bc1 has rank \(1\).

Complex multiplication

The elliptic curves in class 54390.bc do not have complex multiplication.

Modular form 54390.2.a.bc

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - q^{8} + q^{9} - q^{10} - q^{11} + q^{12} + q^{13} + q^{15} + q^{16} - 6 q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display