Properties

Label 230384.by
Number of curves $1$
Conductor $230384$
CM no
Rank $1$

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

Elliptic curves in class 230384.by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
230384.by1 230384by1 \([0, 1, 0, 229376, 118955956]\) \(12562583/64736\) \(-6877532647302496256\) \([]\) \(3041280\) \(2.2967\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 230384.by1 has rank \(1\).

Complex multiplication

The elliptic curves in class 230384.by do not have complex multiplication.

Modular form 230384.2.a.by

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{5} + q^{7} - 2 q^{9} + 3 q^{13} - 2 q^{15} + q^{17} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display