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Properties

Label 3465.r
Number of curves $2$
Conductor $3465$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3465.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3465.r1 3465h2 [0, 0, 1, -241113, 861529329] [] 240000  
3465.r2 3465h1 [0, 0, 1, -80463, -10287981] [] 48000 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3465.r have rank \(1\).

Complex multiplication

The elliptic curves in class 3465.r do not have complex multiplication.

Modular form 3465.2.a.r

sage: E.q_eigenform(10)
 
\( q + 2q^{2} + 2q^{4} - q^{5} + q^{7} - 2q^{10} - q^{11} - 6q^{13} + 2q^{14} - 4q^{16} + 7q^{17} - 5q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.