Properties

Label 18368j
Number of curves $2$
Conductor $18368$
CM no
Rank $0$
Graph

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

Elliptic curves in class 18368j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18368.ba2 18368j1 \([0, 0, 0, -1238572, 488384048]\) \(801581275315909089/70810888830976\) \(18562649641707372544\) \([]\) \(677376\) \(2.4375\) \(\Gamma_0(N)\)-optimal
18368.ba1 18368j2 \([0, 0, 0, -615124012, -5872082306512]\) \(98191033604529537629349729/10906239337336\) \(2859005204846608384\) \([]\) \(4741632\) \(3.4105\)  

Rank

sage: E.rank()
 

The elliptic curves in class 18368j have rank \(0\).

Complex multiplication

The elliptic curves in class 18368j do not have complex multiplication.

Modular form 18368.2.a.j

sage: E.q_eigenform(10)
 
\(q + 3 q^{3} + q^{5} + q^{7} + 6 q^{9} + 2 q^{11} + 3 q^{15} - 3 q^{17} + 8 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.