Properties

Label 14400co
Number of curves $2$
Conductor $14400$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("co1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14400co

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14400.h1 14400co1 \([0, 0, 0, -480, -3800]\) \(131072/9\) \(839808000\) \([2]\) \(6144\) \(0.46063\) \(\Gamma_0(N)\)-optimal
14400.h2 14400co2 \([0, 0, 0, 420, -16400]\) \(5488/81\) \(-120932352000\) \([2]\) \(12288\) \(0.80720\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 14400.2.a.co

sage: E.q_eigenform(10)
 
\(q - 4q^{7} - 4q^{11} + 4q^{17} + O(q^{20})\)  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 Cremona 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 Cremona labels.