Properties

Label 14800.ba
Number of curves $3$
Conductor $14800$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ba1")
 
E.isogeny_class()
 

Elliptic curves in class 14800.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14800.ba1 14800l3 \([0, 1, 0, -749333, 249416963]\) \(727057727488000/37\) \(2368000000\) \([]\) \(62208\) \(1.7199\)  
14800.ba2 14800l2 \([0, 1, 0, -9333, 332963]\) \(1404928000/50653\) \(3241792000000\) \([]\) \(20736\) \(1.1706\)  
14800.ba3 14800l1 \([0, 1, 0, -1333, -19037]\) \(4096000/37\) \(2368000000\) \([]\) \(6912\) \(0.62134\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 14800.ba have rank \(0\).

Complex multiplication

The elliptic curves in class 14800.ba do not have complex multiplication.

Modular form 14800.2.a.ba

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{7} - 2 q^{9} - 3 q^{11} + 4 q^{13} - 6 q^{17} - 2 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.