Properties

Label 93600cn
Number of curves $2$
Conductor $93600$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("cn1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 93600cn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
93600.m2 93600cn1 \([0, 0, 0, -44625, 3625000]\) \(107850176/117\) \(10661625000000\) \([2]\) \(286720\) \(1.4154\) \(\Gamma_0(N)\)-optimal
93600.m1 93600cn2 \([0, 0, 0, -55875, 1656250]\) \(26463592/13689\) \(9979281000000000\) \([2]\) \(573440\) \(1.7620\)  

Rank

sage: E.rank()
 

The elliptic curves in class 93600cn have rank \(0\).

Complex multiplication

The elliptic curves in class 93600cn do not have complex multiplication.

Modular form 93600.2.a.cn

sage: E.q_eigenform(10)
 
\(q - 4q^{7} + 2q^{11} + q^{13} + 2q^{19} + O(q^{20})\)  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 Cremona 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 Cremona labels.