Properties

Label 123840de
Number of curves $2$
Conductor $123840$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("de1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 123840de

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
123840.ei2 123840de1 \([0, 0, 0, -21612, -820816]\) \(5841725401/1857600\) \(354992888217600\) \([2]\) \(442368\) \(1.4958\) \(\Gamma_0(N)\)-optimal
123840.ei1 123840de2 \([0, 0, 0, -136812, 18855344]\) \(1481933914201/53916840\) \(10303668580515840\) \([2]\) \(884736\) \(1.8423\)  

Rank

sage: E.rank()
 

The elliptic curves in class 123840de have rank \(0\).

Complex multiplication

The elliptic curves in class 123840de do not have complex multiplication.

Modular form 123840.2.a.de

sage: E.q_eigenform(10)
 
\(q + q^{5} - 2q^{7} - 2q^{11} + 2q^{13} + 4q^{17} + 6q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.