Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("z1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 12480.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12480.z1 12480ch2 \([0, -1, 0, -2945, 56097]\) \(10779215329/1232010\) \(322964029440\) \([2]\) \(18432\) \(0.94068\)  
12480.z2 12480ch1 \([0, -1, 0, 255, 4257]\) \(6967871/35100\) \(-9201254400\) \([2]\) \(9216\) \(0.59410\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 12480.2.a.z

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.