Properties

Label 26775n
Number of curves $1$
Conductor $26775$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 26775n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26775.k1 26775n1 \([1, -1, 1, -575180, 168045572]\) \(-1995310715276835/9938999\) \(-104825380078125\) \([]\) \(172800\) \(1.8892\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 26775n1 has rank \(1\).

Complex multiplication

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

Modular form 26775.2.a.n

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