Properties

Label 3360.r
Number of curves $2$
Conductor $3360$
CM no
Rank $1$
Graph

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

Elliptic curves in class 3360.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3360.r1 3360j1 \([0, 1, 0, -26, -60]\) \(31554496/525\) \(33600\) \([2]\) \(384\) \(-0.33299\) \(\Gamma_0(N)\)-optimal
3360.r2 3360j2 \([0, 1, 0, -1, -145]\) \(-64/2205\) \(-9031680\) \([2]\) \(768\) \(0.013582\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3360.r have rank \(1\).

Complex multiplication

The elliptic curves in class 3360.r do not have complex multiplication.

Modular form 3360.2.a.r

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.