Properties

Label 32400bz
Number of curves $2$
Conductor $32400$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bz1")
 
E.isogeny_class()
 

Elliptic curves in class 32400bz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32400.f2 32400bz1 \([0, 0, 0, 1725, -2750]\) \(109503/64\) \(-331776000000\) \([]\) \(31104\) \(0.90006\) \(\Gamma_0(N)\)-optimal
32400.f1 32400bz2 \([0, 0, 0, -22275, 1397250]\) \(-35937/4\) \(-136048896000000\) \([]\) \(93312\) \(1.4494\)  

Rank

sage: E.rank()
 

The elliptic curves in class 32400bz have rank \(0\).

Complex multiplication

The elliptic curves in class 32400bz do not have complex multiplication.

Modular form 32400.2.a.bz

sage: E.q_eigenform(10)
 
\(q - 4 q^{7} + q^{13} - 3 q^{17} + 4 q^{19} + O(q^{20})\) 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 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.