Properties

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

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 26775p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26775.e1 26775p1 \([0, 0, 1, -10125, -223594]\) \(14929920/5831\) \(44832645703125\) \([]\) \(86400\) \(1.3182\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 26775p1 has rank \(1\).

Complex multiplication

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

Modular form 26775.2.a.p

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