Properties

Label 32340.r
Number of curves $2$
Conductor $32340$
CM no
Rank $1$
Graph

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

Elliptic curves in class 32340.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32340.r1 32340u2 \([0, -1, 0, -37445, 2801457]\) \(462893166690304/4125\) \(51744000\) \([]\) \(46656\) \(1.0633\)  
32340.r2 32340u1 \([0, -1, 0, -485, 3585]\) \(1007878144/179685\) \(2253968640\) \([]\) \(15552\) \(0.51398\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 32340.r have rank \(1\).

Complex multiplication

The elliptic curves in class 32340.r do not have complex multiplication.

Modular form 32340.2.a.r

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{9} + q^{11} - 5q^{13} - q^{15} - 2q^{19} + O(q^{20})\)  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.