Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 32340t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32340.t2 32340t1 \([0, -1, 0, 12675, -1379223]\) \(7476617216/31444875\) \(-947061273312000\) \([]\) \(124416\) \(1.5563\) \(\Gamma_0(N)\)-optimal
32340.t1 32340t2 \([0, -1, 0, -116685, 42189225]\) \(-5833703071744/22107421875\) \(-665834515500000000\) \([]\) \(373248\) \(2.1056\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 32340.2.a.t

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{9} + q^{11} - 2 q^{13} - q^{15} + 3 q^{17} + 7 q^{19} + O(q^{20})\)  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 Cremona 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 Cremona labels.