Properties

Label 120384cv
Number of curves $2$
Conductor $120384$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cv1")
 
E.isogeny_class()
 

Elliptic curves in class 120384cv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
120384.br2 120384cv1 \([0, 0, 0, -13080, -620714]\) \(-5304438784000/497763387\) \(-23223648583872\) \([]\) \(207360\) \(1.3067\) \(\Gamma_0(N)\)-optimal
120384.br1 120384cv2 \([0, 0, 0, -1082280, -433368722]\) \(-3004935183806464000/2037123\) \(-95044010688\) \([]\) \(622080\) \(1.8561\)  

Rank

sage: E.rank()
 

The elliptic curves in class 120384cv have rank \(0\).

Complex multiplication

The elliptic curves in class 120384cv do not have complex multiplication.

Modular form 120384.2.a.cv

sage: E.q_eigenform(10)
 
\(q - 2 q^{7} - q^{11} + q^{13} - 3 q^{17} + q^{19} + O(q^{20})\) 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.