Properties

Label 38640bt
Number of curves $2$
Conductor $38640$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bt1")
 
E.isogeny_class()
 

Elliptic curves in class 38640bt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38640.bd1 38640bt1 \([0, -1, 0, -3680, 75072]\) \(1345938541921/203765625\) \(834624000000\) \([2]\) \(49152\) \(1.0115\) \(\Gamma_0(N)\)-optimal
38640.bd2 38640bt2 \([0, -1, 0, 6320, 403072]\) \(6814692748079/21258460125\) \(-87074652672000\) \([2]\) \(98304\) \(1.3581\)  

Rank

sage: E.rank()
 

The elliptic curves in class 38640bt have rank \(1\).

Complex multiplication

The elliptic curves in class 38640bt do not have complex multiplication.

Modular form 38640.2.a.bt

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