Properties

Label 14400m
Number of curves 2
Conductor 14400
CM -3
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("14400.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14400m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14400.c2 14400m1 [0, 0, 0, 0, 10] [] 1152 \(\Gamma_0(N)\)-optimal
14400.c1 14400m2 [0, 0, 0, 0, -270] [] 3456  

Rank

sage: E.rank()
 

The elliptic curves in class 14400m have rank \(1\).

Modular form 14400.2.a.c

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.