Properties

Label 48960cd
Number of curves $2$
Conductor $48960$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cd1")
 
E.isogeny_class()
 

Elliptic curves in class 48960cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
48960.cn2 48960cd1 \([0, 0, 0, 229812, 13163888]\) \(7023836099951/4456448000\) \(-851640475189248000\) \([]\) \(483840\) \(2.1295\) \(\Gamma_0(N)\)-optimal
48960.cn1 48960cd2 \([0, 0, 0, -3825228, 2972458352]\) \(-32391289681150609/1228250000000\) \(-234722230272000000000\) \([]\) \(1451520\) \(2.6788\)  

Rank

sage: E.rank()
 

The elliptic curves in class 48960cd have rank \(1\).

Complex multiplication

The elliptic curves in class 48960cd do not have complex multiplication.

Modular form 48960.2.a.cd

sage: E.q_eigenform(10)
 
\(q - q^{5} + 2 q^{7} + q^{13} + q^{17} + q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.