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Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("cp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 148225cp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
148225.co2 148225cp1 [1, 1, 0, -36775, 2699250] [] 302400 \(\Gamma_0(N)\)-optimal
148225.co1 148225cp2 [1, 1, 0, -373650, -343810375] [] 3326400  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 148225.2.a.cp

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.