Properties

Label 2925.k
Number of curves $2$
Conductor $2925$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2925.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2925.k1 2925a2 \([0, 0, 1, -9450, -355219]\) \(-303464448/1625\) \(-499763671875\) \([]\) \(3456\) \(1.0893\)  
2925.k2 2925a1 \([0, 0, 1, 300, -2594]\) \(7077888/10985\) \(-4634296875\) \([]\) \(1152\) \(0.54000\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2925.k have rank \(1\).

Complex multiplication

The elliptic curves in class 2925.k do not have complex multiplication.

Modular form 2925.2.a.k

sage: E.q_eigenform(10)
 
\(q - 2 q^{4} + q^{7} + 3 q^{11} - q^{13} + 4 q^{16} - 3 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.