Properties

Label 14400.dp
Number of curves $2$
Conductor $14400$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("dp1")
 
E.isogeny_class()
 

Elliptic curves in class 14400.dp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14400.dp1 14400es2 \([0, 0, 0, -43500, 3350000]\) \(195112/9\) \(419904000000000\) \([2]\) \(61440\) \(1.5674\)  
14400.dp2 14400es1 \([0, 0, 0, 1500, 200000]\) \(64/3\) \(-17496000000000\) \([2]\) \(30720\) \(1.2208\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 14400.2.a.dp

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.