Properties

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

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 26775.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26775.s1 26775h1 \([1, -1, 1, -207065, -36215018]\) \(-1995310715276835/9938999\) \(-4890732932925\) \([]\) \(103680\) \(1.6338\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 26775.s1 has rank \(1\).

Complex multiplication

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

Modular form 26775.2.a.s

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