Properties

Label 7200.ba
Number of curves $4$
Conductor $7200$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ba1")
 
E.isogeny_class()
 

Elliptic curves in class 7200.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7200.ba1 7200bf2 \([0, 0, 0, -36075, -2637250]\) \(890277128/15\) \(87480000000\) \([2]\) \(12288\) \(1.2298\)  
7200.ba2 7200bf3 \([0, 0, 0, -9075, 292250]\) \(14172488/1875\) \(10935000000000\) \([2]\) \(12288\) \(1.2298\)  
7200.ba3 7200bf1 \([0, 0, 0, -2325, -38500]\) \(1906624/225\) \(164025000000\) \([2, 2]\) \(6144\) \(0.88325\) \(\Gamma_0(N)\)-optimal
7200.ba4 7200bf4 \([0, 0, 0, 3300, -196000]\) \(85184/405\) \(-18895680000000\) \([2]\) \(12288\) \(1.2298\)  

Rank

sage: E.rank()
 

The elliptic curves in class 7200.ba have rank \(1\).

Complex multiplication

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

Modular form 7200.2.a.ba

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

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.