Properties

Label 271440p
Number of curves $1$
Conductor $271440$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 271440p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
271440.p1 271440p1 \([0, 0, 0, -7162923, 7386252122]\) \(-13611534355369215721/15998696220000\) \(-47771850933780480000\) \([]\) \(9523200\) \(2.6880\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 271440p1 has rank \(1\).

Complex multiplication

The elliptic curves in class 271440p do not have complex multiplication.

Modular form 271440.2.a.p

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