Properties

Label 26775.f
Number of curves $1$
Conductor $26775$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 26775.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26775.f1 26775j1 \([0, 0, 1, -45, 66]\) \(14929920/5831\) \(3935925\) \([]\) \(5760\) \(-0.035818\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 26775.f1 has rank \(1\).

Complex multiplication

The elliptic curves in class 26775.f do not have complex multiplication.

Modular form 26775.2.a.f

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