Properties

Label 18496b
Number of curves $2$
Conductor $18496$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("18496.l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 18496b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
18496.l1 18496b1 [0, 0, 0, -5780, -157216] [2] 18432 \(\Gamma_0(N)\)-optimal
18496.l2 18496b2 [0, 0, 0, 5780, -707472] [2] 36864  

Rank

sage: E.rank()
 

The elliptic curves in class 18496b have rank \(1\).

Modular form 18496.2.a.l

sage: E.q_eigenform(10)
 
\( q - 2q^{7} - 3q^{9} + 4q^{11} - 2q^{13} - 4q^{19} + O(q^{20}) \)

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.