Properties

Label 14400.j
Number of curves $4$
Conductor $14400$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14400.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14400.j1 14400bu3 \([0, 0, 0, -446700, -63974000]\) \(26410345352/10546875\) \(3936600000000000000\) \([2]\) \(294912\) \(2.2662\)  
14400.j2 14400bu2 \([0, 0, 0, -203700, 34684000]\) \(20034997696/455625\) \(21257640000000000\) \([2, 2]\) \(147456\) \(1.9197\)  
14400.j3 14400bu1 \([0, 0, 0, -202575, 35093500]\) \(1261112198464/675\) \(492075000000\) \([2]\) \(73728\) \(1.5731\) \(\Gamma_0(N)\)-optimal
14400.j4 14400bu4 \([0, 0, 0, 21300, 107134000]\) \(2863288/13286025\) \(-4958982259200000000\) \([2]\) \(294912\) \(2.2662\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 14400.2.a.j

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.