Properties

Label 32200u
Number of curves $2$
Conductor $32200$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 32200u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32200.f2 32200u1 \([0, 1, 0, -708, 9088]\) \(-9826000/3703\) \(-14812000000\) \([2]\) \(23040\) \(0.66139\) \(\Gamma_0(N)\)-optimal
32200.f1 32200u2 \([0, 1, 0, -12208, 515088]\) \(12576878500/1127\) \(18032000000\) \([2]\) \(46080\) \(1.0080\)  

Rank

sage: E.rank()
 

The elliptic curves in class 32200u have rank \(1\).

Complex multiplication

The elliptic curves in class 32200u do not have complex multiplication.

Modular form 32200.2.a.u

sage: E.q_eigenform(10)
 
\(q - 2q^{3} + q^{7} + q^{9} + 4q^{11} - 6q^{13} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.