Properties

Label 71058c
Number of curves $1$
Conductor $71058$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 71058c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
71058.a1 71058c1 \([1, 1, 0, -26082, -1584012]\) \(1962331615744816681/66502247645184\) \(66502247645184\) \([]\) \(271360\) \(1.4246\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 71058c1 has rank \(1\).

Complex multiplication

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

Modular form 71058.2.a.c

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