Properties

Label 59200.dm
Number of curves $4$
Conductor $59200$
CM no
Rank $1$
Graph

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

Elliptic curves in class 59200.dm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
59200.dm1 59200cz3 \([0, -1, 0, -8440033, 9440471937]\) \(16232905099479601/4052240\) \(16597975040000000\) \([2]\) \(1327104\) \(2.4879\)  
59200.dm2 59200cz4 \([0, -1, 0, -8408033, 9515575937]\) \(-16048965315233521/256572640900\) \(-1050921537126400000000\) \([2]\) \(2654208\) \(2.8345\)  
59200.dm3 59200cz1 \([0, -1, 0, -120033, 8791937]\) \(46694890801/18944000\) \(77594624000000000\) \([2]\) \(442368\) \(1.9386\) \(\Gamma_0(N)\)-optimal
59200.dm4 59200cz2 \([0, -1, 0, 391967, 63575937]\) \(1625964918479/1369000000\) \(-5607424000000000000\) \([2]\) \(884736\) \(2.2852\)  

Rank

sage: E.rank()
 

The elliptic curves in class 59200.dm have rank \(1\).

Complex multiplication

The elliptic curves in class 59200.dm do not have complex multiplication.

Modular form 59200.2.a.dm

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.