Properties

Label 14400.cq
Number of curves $2$
Conductor $14400$
CM \(\Q(\sqrt{-1}) \)
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cq1")
 
E.isogeny_class()
 

Elliptic curves in class 14400.cq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality CM discriminant
14400.cq1 14400de1 \([0, 0, 0, -15, 0]\) \(1728\) \(216000\) \([2]\) \(1024\) \(-0.28695\) \(\Gamma_0(N)\)-optimal \(-4\)
14400.cq2 14400de2 \([0, 0, 0, 60, 0]\) \(1728\) \(-13824000\) \([2]\) \(2048\) \(0.059627\)   \(-4\)

Rank

sage: E.rank()
 

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

Complex multiplication

Each elliptic curve in class 14400.cq has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-1}) \).

Modular form 14400.2.a.cq

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