Properties

Label 54978.z
Number of curves $1$
Conductor $54978$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 54978.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54978.z1 54978s1 \([1, 0, 1, -1888, -178510]\) \(-6321363049/113144724\) \(-13311363633876\) \([]\) \(122880\) \(1.1994\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 54978.z1 has rank \(1\).

Complex multiplication

The elliptic curves in class 54978.z do not have complex multiplication.

Modular form 54978.2.a.z

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