Properties

Label 51600.dm
Number of curves $2$
Conductor $51600$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("dm1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 51600.dm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51600.dm1 51600dg2 \([0, 1, 0, -893333, 324792963]\) \(-1971080396800/715563\) \(-28622520000000000\) \([]\) \(440640\) \(2.1263\)  
51600.dm2 51600dg1 \([0, 1, 0, 6667, 1692963]\) \(819200/31347\) \(-1253880000000000\) \([]\) \(146880\) \(1.5770\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 51600.dm have rank \(0\).

Complex multiplication

The elliptic curves in class 51600.dm do not have complex multiplication.

Modular form 51600.2.a.dm

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.