Properties

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

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 7200.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7200.b1 7200bp3 \([0, 0, 0, -108075, 13675250]\) \(23937672968/45\) \(262440000000\) \([2]\) \(24576\) \(1.4463\)  
7200.b2 7200bp2 \([0, 0, 0, -18075, -657250]\) \(111980168/32805\) \(191318760000000\) \([2]\) \(24576\) \(1.4463\)  
7200.b3 7200bp1 \([0, 0, 0, -6825, 209000]\) \(48228544/2025\) \(1476225000000\) \([2, 2]\) \(12288\) \(1.0998\) \(\Gamma_0(N)\)-optimal
7200.b4 7200bp4 \([0, 0, 0, 3300, 776000]\) \(85184/5625\) \(-262440000000000\) \([2]\) \(24576\) \(1.4463\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 7200.2.a.b

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.