Properties

Label 12480.by
Number of curves $1$
Conductor $12480$
CM no
Rank $1$

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

Elliptic curves in class 12480.by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12480.by1 12480z1 \([0, 1, 0, -31, 59]\) \(-53157376/1755\) \(-112320\) \([]\) \(1152\) \(-0.25616\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 12480.by1 has rank \(1\).

Complex multiplication

The elliptic curves in class 12480.by do not have complex multiplication.

Modular form 12480.2.a.by

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} - q^{7} + q^{9} + q^{11} + q^{13} - q^{15} - 5 q^{17} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display