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Properties

Label 148225be
Number of curves $2$
Conductor $148225$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("be1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 148225be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
148225.be2 148225be1 [1, 1, 1, -3088, 256906] [] 302400 \(\Gamma_0(N)\)-optimal
148225.be1 148225be2 [1, 1, 1, -4449838, -3614950844] [] 3326400  

Rank

sage: E.rank()
 

The elliptic curves in class 148225be have rank \(1\).

Complex multiplication

The elliptic curves in class 148225be do not have complex multiplication.

Modular form 148225.2.a.be

sage: E.q_eigenform(10)
 
\( q - q^{2} + 2q^{3} - q^{4} - 2q^{6} + 3q^{8} + q^{9} - 2q^{12} + q^{13} - q^{16} - 5q^{17} - q^{18} - 6q^{19} + O(q^{20}) \)

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.