Properties

Label 271040cr
Number of curves $1$
Conductor $271040$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("cr1")
 
E.isogeny_class()
 

Elliptic curves in class 271040cr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
271040.cr1 271040cr1 \([0, -1, 0, -9115, -332275]\) \(-738763264/875\) \(-99207416000\) \([]\) \(274560\) \(1.0216\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 271040cr1 has rank \(1\).

Complex multiplication

The elliptic curves in class 271040cr do not have complex multiplication.

Modular form 271040.2.a.cr

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{7} - 2 q^{9} - q^{13} - q^{15} - q^{17} + O(q^{20})\) Copy content Toggle raw display