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Properties

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

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Show commands: SageMath
Copy content sage:E = EllipticCurve("pg1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 486720.pg1 has rank \(0\).

Complex multiplication

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

Modular form 486720.2.a.pg

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

Elliptic curves in class 486720.pg

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
486720.pg1 486720pg1 \([0, 0, 0, -342732, 77000456]\) \(7311616/25\) \(15223493007590400\) \([]\) \(4792320\) \(1.9686\) \(\Gamma_0(N)\)-optimal