Properties

Label 487872.pe
Number of curves $1$
Conductor $487872$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("pe1")
 
E.isogeny_class()
 

Elliptic curves in class 487872.pe

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
487872.pe1 487872pe1 \([0, 0, 0, 68244, 16365008]\) \(50250332/194481\) \(-136036477698637824\) \([]\) \(3932160\) \(1.9704\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 487872.pe1 has rank \(0\).

Complex multiplication

The elliptic curves in class 487872.pe do not have complex multiplication.

Modular form 487872.2.a.pe

sage: E.q_eigenform(10)
 
\(q + 3 q^{5} - q^{7} + q^{13} + 5 q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display