Properties

Label 7488bt
Number of curves $4$
Conductor $7488$
CM no
Rank $1$
Graph

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

Elliptic curves in class 7488bt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7488.bk4 7488bt1 \([0, 0, 0, -11244, 9580880]\) \(-822656953/207028224\) \(-39563709722394624\) \([2]\) \(61440\) \(1.8640\) \(\Gamma_0(N)\)-optimal
7488.bk3 7488bt2 \([0, 0, 0, -748524, 246985040]\) \(242702053576633/2554695936\) \(488209996144705536\) \([2, 2]\) \(122880\) \(2.2105\)  
7488.bk2 7488bt3 \([0, 0, 0, -1347564, -204211888]\) \(1416134368422073/725251155408\) \(138597654145907294208\) \([2]\) \(245760\) \(2.5571\)  
7488.bk1 7488bt4 \([0, 0, 0, -11945964, 15892048208]\) \(986551739719628473/111045168\) \(21221062075219968\) \([2]\) \(245760\) \(2.5571\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 7488.2.a.bt

sage: E.q_eigenform(10)
 
\(q + 2 q^{5} - 4 q^{7} + 4 q^{11} - q^{13} - 2 q^{17} - 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.