Properties

Label 7200bt
Number of curves $2$
Conductor $7200$
CM no
Rank $0$
Graph

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

Elliptic curves in class 7200bt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7200.br2 7200bt1 \([0, 0, 0, 375, 25000]\) \(64/3\) \(-273375000000\) \([2]\) \(7680\) \(0.87427\) \(\Gamma_0(N)\)-optimal
7200.br1 7200bt2 \([0, 0, 0, -10875, 418750]\) \(195112/9\) \(6561000000000\) \([2]\) \(15360\) \(1.2208\)  

Rank

sage: E.rank()
 

The elliptic curves in class 7200bt have rank \(0\).

Complex multiplication

The elliptic curves in class 7200bt do not have complex multiplication.

Modular form 7200.2.a.bt

sage: E.q_eigenform(10)
 
\(q + 2 q^{7} + 6 q^{11} - 2 q^{13} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.