Properties

Label 257600by
Number of curves $1$
Conductor $257600$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("by1")
 
E.isogeny_class()
 

Elliptic curves in class 257600by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
257600.by1 257600by1 \([0, -1, 0, -1540833, -1772110463]\) \(-158034076225/438790688\) \(-1123304161280000000000\) \([]\) \(9216000\) \(2.7265\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 257600by1 has rank \(0\).

Complex multiplication

The elliptic curves in class 257600by do not have complex multiplication.

Modular form 257600.2.a.by

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{7} - 2 q^{9} - 5 q^{11} + 2 q^{13} + 5 q^{17} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display