Properties

Label 14400.cz
Number of curves $8$
Conductor $14400$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cz1")
 
E.isogeny_class()
 

Elliptic curves in class 14400.cz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14400.cz1 14400dp7 \([0, 0, 0, -31104300, -66769598000]\) \(1114544804970241/405\) \(1209323520000000\) \([2]\) \(393216\) \(2.6846\)  
14400.cz2 14400dp5 \([0, 0, 0, -1944300, -1042958000]\) \(272223782641/164025\) \(489776025600000000\) \([2, 2]\) \(196608\) \(2.3380\)  
14400.cz3 14400dp8 \([0, 0, 0, -1584300, -1441118000]\) \(-147281603041/215233605\) \(-642684100792320000000\) \([2]\) \(393216\) \(2.6846\)  
14400.cz4 14400dp4 \([0, 0, 0, -1152300, 476098000]\) \(56667352321/15\) \(44789760000000\) \([2]\) \(98304\) \(1.9915\)  
14400.cz5 14400dp3 \([0, 0, 0, -144300, -9758000]\) \(111284641/50625\) \(151165440000000000\) \([2, 2]\) \(98304\) \(1.9915\)  
14400.cz6 14400dp2 \([0, 0, 0, -72300, 7378000]\) \(13997521/225\) \(671846400000000\) \([2, 2]\) \(49152\) \(1.6449\)  
14400.cz7 14400dp1 \([0, 0, 0, -300, 322000]\) \(-1/15\) \(-44789760000000\) \([2]\) \(24576\) \(1.2983\) \(\Gamma_0(N)\)-optimal
14400.cz8 14400dp6 \([0, 0, 0, 503700, -73262000]\) \(4733169839/3515625\) \(-10497600000000000000\) \([2]\) \(196608\) \(2.3380\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 14400.2.a.cz

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

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.