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Properties

Label 486720.po
Number of curves $1$
Conductor $486720$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("po1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 486720.po1 has rank \(0\).

Complex multiplication

The elliptic curves in class 486720.po do not have complex multiplication.

Modular form 486720.2.a.po

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

Elliptic curves in class 486720.po

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
486720.po1 486720po1 \([0, 0, 0, -12997452, 42901363856]\) \(-1557701041/4199040\) \(-654582334244786106531840\) \([]\) \(53673984\) \(3.2573\) \(\Gamma_0(N)\)-optimal