Properties

Label 137280.db
Number of curves $2$
Conductor $137280$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("db1")
 
E.isogeny_class()
 

Elliptic curves in class 137280.db

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
137280.db1 137280co2 \([0, -1, 0, -1876865, 990312225]\) \(2789222297765780449/677605500\) \(177630216192000\) \([2]\) \(1769472\) \(2.1115\)  
137280.db2 137280co1 \([0, -1, 0, -116865, 15624225]\) \(-673350049820449/10617750000\) \(-2783379456000000\) \([2]\) \(884736\) \(1.7649\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 137280.db have rank \(1\).

Complex multiplication

The elliptic curves in class 137280.db do not have complex multiplication.

Modular form 137280.2.a.db

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