Properties

Label 5415.c
Number of curves $2$
Conductor $5415$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 5415.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5415.c1 5415h2 \([1, 0, 0, -33761, 2323110]\) \(90458382169/2671875\) \(125700713296875\) \([2]\) \(17280\) \(1.4826\)  
5415.c2 5415h1 \([1, 0, 0, 534, 121371]\) \(357911/135375\) \(-6368836140375\) \([2]\) \(8640\) \(1.1360\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5415.c have rank \(1\).

Complex multiplication

The elliptic curves in class 5415.c do not have complex multiplication.

Modular form 5415.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} - q^{4} - q^{5} - q^{6} - 2 q^{7} + 3 q^{8} + q^{9} + q^{10} - 2 q^{11} - q^{12} + 4 q^{13} + 2 q^{14} - q^{15} - q^{16} + 2 q^{17} - q^{18} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.