Properties

Label 286110.ce
Number of curves $1$
Conductor $286110$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("ce1")
 
E.isogeny_class()
 

Elliptic curves in class 286110.ce

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
286110.ce1 286110ce1 \([1, -1, 0, 5080566, 12072893940]\) \(22253722294800933/109514680000000\) \(-71372289915348840000000\) \([]\) \(29030400\) \(3.0674\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 286110.ce1 has rank \(1\).

Complex multiplication

The elliptic curves in class 286110.ce do not have complex multiplication.

Modular form 286110.2.a.ce

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