Properties

Label 14400bp
Number of curves $4$
Conductor $14400$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bp1")
 
E.isogeny_class()
 

Elliptic curves in class 14400bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14400.fd3 14400bp1 \([0, 0, 0, -1800, -27000]\) \(55296/5\) \(58320000000\) \([2]\) \(12288\) \(0.80524\) \(\Gamma_0(N)\)-optimal
14400.fd2 14400bp2 \([0, 0, 0, -6300, 162000]\) \(148176/25\) \(4665600000000\) \([2, 2]\) \(24576\) \(1.1518\)  
14400.fd1 14400bp3 \([0, 0, 0, -96300, 11502000]\) \(132304644/5\) \(3732480000000\) \([2]\) \(49152\) \(1.4984\)  
14400.fd4 14400bp4 \([0, 0, 0, 11700, 918000]\) \(237276/625\) \(-466560000000000\) \([2]\) \(49152\) \(1.4984\)  

Rank

sage: E.rank()
 

The elliptic curves in class 14400bp have rank \(0\).

Complex multiplication

The elliptic curves in class 14400bp do not have complex multiplication.

Modular form 14400.2.a.bp

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.