Properties

Label 67270.o
Number of curves $1$
Conductor $67270$
CM no
Rank $1$

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

Elliptic curves in class 67270.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
67270.o1 67270f1 \([1, 0, 1, -1369, -17558]\) \(9514651159/1093750\) \(32583906250\) \([]\) \(60928\) \(0.74936\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 67270.o1 has rank \(1\).

Complex multiplication

The elliptic curves in class 67270.o do not have complex multiplication.

Modular form 67270.2.a.o

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} + q^{7} - q^{8} - 2 q^{9} + q^{10} - 3 q^{11} + q^{12} + 5 q^{13} - q^{14} - q^{15} + q^{16} - 2 q^{17} + 2 q^{18} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display