Properties

Label 14400.n
Number of curves $4$
Conductor $14400$
CM \(\Q(\sqrt{-3}) \)
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14400.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality CM discriminant
14400.n1 14400cz4 \([0, 0, 0, -13500, 594000]\) \(54000\) \(5038848000000\) \([2]\) \(27648\) \(1.2318\)   \(-12\)
14400.n2 14400cz2 \([0, 0, 0, -1500, -22000]\) \(54000\) \(6912000000\) \([2]\) \(9216\) \(0.68245\)   \(-12\)
14400.n3 14400cz1 \([0, 0, 0, 0, -1000]\) \(0\) \(-432000000\) \([2]\) \(4608\) \(0.33588\) \(\Gamma_0(N)\)-optimal \(-3\)
14400.n4 14400cz3 \([0, 0, 0, 0, 27000]\) \(0\) \(-314928000000\) \([2]\) \(13824\) \(0.88518\)   \(-3\)

Rank

sage: E.rank()
 

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

Complex multiplication

Each elliptic curve in class 14400.n has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).

Modular form 14400.2.a.n

sage: E.q_eigenform(10)
 
\(q - 4q^{7} + 2q^{13} + 8q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.