Properties

Label 67158.r
Number of curves $1$
Conductor $67158$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 67158.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
67158.r1 67158f1 \([1, -1, 0, -3498868644, 79660744553456]\) \(-240666329650344616245541600467/13684675140196339552\) \(-269355460784484551402016\) \([]\) \(36028800\) \(3.9624\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 67158.r1 has rank \(0\).

Complex multiplication

The elliptic curves in class 67158.r do not have complex multiplication.

Modular form 67158.2.a.r

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