Properties

Label 37200by
Number of curves $1$
Conductor $37200$
CM no
Rank $1$

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

Elliptic curves in class 37200by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37200.bq1 37200by1 \([0, -1, 0, 38992, -1639488]\) \(102437538839/77137920\) \(-4936826880000000\) \([]\) \(253440\) \(1.6995\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 37200by1 has rank \(1\).

Complex multiplication

The elliptic curves in class 37200by do not have complex multiplication.

Modular form 37200.2.a.by

sage: E.q_eigenform(10)
 
\(q - q^{3} + 3 q^{7} + q^{9} - 3 q^{11} + 2 q^{13} - 8 q^{17} + 7 q^{19} + O(q^{20})\) Copy content Toggle raw display