Properties

Label 71058.o
Number of curves $1$
Conductor $71058$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 71058.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
71058.o1 71058n1 \([1, 0, 0, -89, 297]\) \(78018694417/5116176\) \(5116176\) \([]\) \(16128\) \(0.037062\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 71058.o1 has rank \(1\).

Complex multiplication

The elliptic curves in class 71058.o do not have complex multiplication.

Modular form 71058.2.a.o

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + 3 q^{5} + q^{6} - q^{7} + q^{8} + q^{9} + 3 q^{10} + 2 q^{11} + q^{12} + q^{13} - q^{14} + 3 q^{15} + q^{16} - 3 q^{17} + q^{18} + O(q^{20})\) Copy content Toggle raw display