Properties

Label 18496p
Number of curves $2$
Conductor $18496$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 18496p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18496.o1 18496p1 \([0, -1, 0, -5009, -53647]\) \(35152/17\) \(6722988818432\) \([2]\) \(36864\) \(1.1550\) \(\Gamma_0(N)\)-optimal
18496.o2 18496p2 \([0, -1, 0, 18111, -428191]\) \(415292/289\) \(-457163239653376\) \([2]\) \(73728\) \(1.5016\)  

Rank

sage: E.rank()
 

The elliptic curves in class 18496p have rank \(0\).

Complex multiplication

The elliptic curves in class 18496p do not have complex multiplication.

Modular form 18496.2.a.p

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} - 2 q^{5} - 2 q^{7} + q^{9} + 6 q^{11} - 2 q^{13} - 4 q^{15} + O(q^{20})\) 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 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.