Properties

Label 272734.z
Number of curves $1$
Conductor $272734$
CM no
Rank $0$

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

Elliptic curves in class 272734.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
272734.z1 272734z1 \([1, -1, 0, -21863, -750667]\) \(5545233/2024\) \(421846897300136\) \([]\) \(950400\) \(1.5067\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 272734.z1 has rank \(0\).

Complex multiplication

The elliptic curves in class 272734.z do not have complex multiplication.

Modular form 272734.2.a.z

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