Properties

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

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 67270.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
67270.j1 67270g1 \([1, 1, 0, -1315148, 519117502]\) \(9514651159/1093750\) \(28918336738233906250\) \([]\) \(1888768\) \(2.4664\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 67270.j1 has rank \(1\).

Complex multiplication

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

Modular form 67270.2.a.j

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