Properties

Label 12480.df
Number of curves $2$
Conductor $12480$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("df1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 12480.df

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12480.df1 12480bk2 \([0, 1, 0, -2945, -56097]\) \(10779215329/1232010\) \(322964029440\) \([2]\) \(18432\) \(0.94068\)  
12480.df2 12480bk1 \([0, 1, 0, 255, -4257]\) \(6967871/35100\) \(-9201254400\) \([2]\) \(9216\) \(0.59410\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 12480.df have rank \(0\).

Complex multiplication

The elliptic curves in class 12480.df do not have complex multiplication.

Modular form 12480.2.a.df

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + 2q^{7} + q^{9} - 4q^{11} + q^{13} + q^{15} + 8q^{17} + 6q^{19} + O(q^{20})\)  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 LMFDB 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 LMFDB labels.