Properties

Label 193200.gz
Number of curves $2$
Conductor $193200$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("gz1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 193200.gz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
193200.gz1 193200bm1 \([0, 1, 0, -9408, -196812]\) \(1439069689/579600\) \(37094400000000\) \([2]\) \(442368\) \(1.3017\) \(\Gamma_0(N)\)-optimal
193200.gz2 193200bm2 \([0, 1, 0, 30592, -1396812]\) \(49471280711/41992020\) \(-2687489280000000\) \([2]\) \(884736\) \(1.6482\)  

Rank

sage: E.rank()
 

The elliptic curves in class 193200.gz have rank \(0\).

Complex multiplication

The elliptic curves in class 193200.gz do not have complex multiplication.

Modular form 193200.2.a.gz

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{7} + q^{9} + 2q^{11} - 4q^{13} + 6q^{17} + 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.