Properties

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

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 32340.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32340.a1 32340c2 \([0, -1, 0, -396426, 96212061]\) \(-8788102954619113216/954968814855\) \(-748695550846320\) \([]\) \(279936\) \(1.8840\)  
32340.a2 32340c1 \([0, -1, 0, 474, 400401]\) \(14990845184/88418496375\) \(-69320101158000\) \([]\) \(93312\) \(1.3347\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 32340.2.a.a

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