Properties

Label 7488.bo
Number of curves $2$
Conductor $7488$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bo1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7488.bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7488.bo1 7488ba2 \([0, 0, 0, -104484, -12995552]\) \(42246001231552/14414517\) \(43041517129728\) \([2]\) \(24576\) \(1.5877\)  
7488.bo2 7488ba1 \([0, 0, 0, -5619, -261740]\) \(-420526439488/390971529\) \(-18241167657024\) \([2]\) \(12288\) \(1.2411\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7488.bo have rank \(1\).

Complex multiplication

The elliptic curves in class 7488.bo do not have complex multiplication.

Modular form 7488.2.a.bo

sage: E.q_eigenform(10)
 
\(q + 2q^{5} - 2q^{7} + 2q^{11} + q^{13} - 6q^{17} + 2q^{19} + O(q^{20})\)  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.