Properties

Label 17424ce
Number of curves $2$
Conductor $17424$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ce1")
 
E.isogeny_class()
 

Elliptic curves in class 17424ce

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17424.f2 17424ce1 \([0, 0, 0, -4719, -142054]\) \(-4253392/729\) \(-1991891886336\) \([]\) \(32256\) \(1.0864\) \(\Gamma_0(N)\)-optimal
17424.f1 17424ce2 \([0, 0, 0, -396759, -96191854]\) \(-2527934627152/9\) \(-24591257856\) \([]\) \(96768\) \(1.6357\)  

Rank

sage: E.rank()
 

The elliptic curves in class 17424ce have rank \(0\).

Complex multiplication

The elliptic curves in class 17424ce do not have complex multiplication.

Modular form 17424.2.a.ce

sage: E.q_eigenform(10)
 
\(q - 3 q^{5} - 2 q^{7} + 5 q^{13} + 3 q^{17} + 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.