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Properties

Label 16905l
Number of curves $4$
Conductor $16905$
CM no
Rank $1$
Graph

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

Elliptic curves in class 16905l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16905.x4 16905l1 \([1, 1, 0, 22368, -801261]\) \(10519294081031/8500170375\) \(-1000036544448375\) \([2]\) \(86400\) \(1.5661\) \(\Gamma_0(N)\)-optimal
16905.x3 16905l2 \([1, 1, 0, -107237, -7100064]\) \(1159246431432649/488076890625\) \(57421758105140625\) \([2, 2]\) \(172800\) \(1.9127\)  
16905.x1 16905l3 \([1, 1, 0, -1476542, -690930981]\) \(3026030815665395929/1364501953125\) \(160532290283203125\) \([2]\) \(345600\) \(2.2592\)  
16905.x2 16905l4 \([1, 1, 0, -811612, 276199561]\) \(502552788401502649/10024505152875\) \(1179373006730590875\) \([2]\) \(345600\) \(2.2592\)  

Rank

sage: E.rank()
 

The elliptic curves in class 16905l have rank \(1\).

Complex multiplication

The elliptic curves in class 16905l do not have complex multiplication.

Modular form 16905.2.a.l

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - 3 q^{8} + q^{9} + q^{10} + 4 q^{11} + q^{12} - 6 q^{13} - q^{15} - q^{16} + 2 q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.