Properties

Label 369600ma
Number of curves $2$
Conductor $369600$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ma1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 369600ma

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
369600.ma2 369600ma1 [0, 1, 0, -894033, 380738313] [] 11520000 \(\Gamma_0(N)\)-optimal
369600.ma1 369600ma2 [0, 1, 0, -2679033, -31909386687] [] 57600000  

Rank

sage: E.rank()
 

The elliptic curves in class 369600ma have rank \(0\).

Complex multiplication

The elliptic curves in class 369600ma do not have complex multiplication.

Modular form 369600.2.a.ma

sage: E.q_eigenform(10)
 
\( q + q^{3} - q^{7} + q^{9} - q^{11} - 6q^{13} + 7q^{17} + 5q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.