Properties

Label 14400.e
Number of curves $2$
Conductor $14400$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 14400.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14400.e1 14400t2 \([0, 0, 0, -1260, 17200]\) \(1000188\) \(221184000\) \([2]\) \(8192\) \(0.52064\)  
14400.e2 14400t1 \([0, 0, 0, -60, 400]\) \(-432\) \(-55296000\) \([2]\) \(4096\) \(0.17407\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 14400.e have rank \(2\).

Complex multiplication

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

Modular form 14400.2.a.e

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