Properties

Label 17424.bu
Number of curves $6$
Conductor $17424$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 17424.bu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17424.bu1 17424t5 \([0, 0, 0, -418539, 104219962]\) \(3065617154/9\) \(23804337604608\) \([2]\) \(81920\) \(1.7960\)  
17424.bu2 17424t3 \([0, 0, 0, -70059, -7136822]\) \(28756228/3\) \(3967389600768\) \([2]\) \(40960\) \(1.4495\)  
17424.bu3 17424t4 \([0, 0, 0, -26499, 1583890]\) \(1556068/81\) \(107119519220736\) \([2, 2]\) \(40960\) \(1.4495\)  
17424.bu4 17424t2 \([0, 0, 0, -4719, -93170]\) \(35152/9\) \(2975542200576\) \([2, 2]\) \(20480\) \(1.1029\)  
17424.bu5 17424t1 \([0, 0, 0, 726, -9317]\) \(2048/3\) \(-61990462512\) \([2]\) \(10240\) \(0.75633\) \(\Gamma_0(N)\)-optimal
17424.bu6 17424t6 \([0, 0, 0, 17061, 6279658]\) \(207646/6561\) \(-17353362113759232\) \([2]\) \(81920\) \(1.7960\)  

Rank

sage: E.rank()
 

The elliptic curves in class 17424.bu have rank \(1\).

Complex multiplication

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

Modular form 17424.2.a.bu

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

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.