Properties

Label 18515.n
Number of curves $2$
Conductor $18515$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 18515.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18515.n1 18515j2 \([0, 1, 1, -1625, 24679]\) \(-897625882624/875\) \(-462875\) \([]\) \(6048\) \(0.38098\)  
18515.n2 18515j1 \([0, 1, 1, -15, 46]\) \(-753664/1715\) \(-907235\) \([]\) \(2016\) \(-0.16832\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 18515.n have rank \(1\).

Complex multiplication

The elliptic curves in class 18515.n do not have complex multiplication.

Modular form 18515.2.a.n

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{4} + q^{5} - q^{7} - 2 q^{9} - 3 q^{11} - 2 q^{12} - q^{13} + q^{15} + 4 q^{16} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.