Properties

Label 54390b
Number of curves $1$
Conductor $54390$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 54390b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54390.g1 54390b1 \([1, 1, 0, -19598898, 33391788858]\) \(-144422342436306640489/19351653425550\) \(-111558431019264065550\) \([]\) \(6420960\) \(2.8658\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 54390b1 has rank \(1\).

Complex multiplication

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

Modular form 54390.2.a.b

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