Properties

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

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Show commands: SageMath
E = EllipticCurve("bh1")
 
E.isogeny_class()
 

Elliptic curves in class 14400bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14400.bf3 14400bh1 \([0, 0, 0, -1740, -33680]\) \(-121945/32\) \(-152882380800\) \([]\) \(11520\) \(0.86293\) \(\Gamma_0(N)\)-optimal
14400.bf4 14400bh2 \([0, 0, 0, 12660, 248560]\) \(46969655/32768\) \(-156551557939200\) \([]\) \(34560\) \(1.4122\)  
14400.bf2 14400bh3 \([0, 0, 0, -7500, 2950000]\) \(-25/2\) \(-3732480000000000\) \([]\) \(57600\) \(1.6676\)  
14400.bf1 14400bh4 \([0, 0, 0, -1807500, 935350000]\) \(-349938025/8\) \(-14929920000000000\) \([]\) \(172800\) \(2.2170\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 14400.2.a.bh

sage: E.q_eigenform(10)
 
\(q - 2 q^{7} - 3 q^{11} - 4 q^{13} - 3 q^{17} - 5 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 3 & 5 & 15 \\ 3 & 1 & 15 & 5 \\ 5 & 15 & 1 & 3 \\ 15 & 5 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.