Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 93600f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
93600.bg2 93600f1 \([0, 0, 0, 6075, 580500]\) \(1259712/8125\) \(-159924375000000\) \([2]\) \(221184\) \(1.4073\) \(\Gamma_0(N)\)-optimal
93600.bg1 93600f2 \([0, 0, 0, -78300, 7668000]\) \(42144192/4225\) \(5322283200000000\) \([2]\) \(442368\) \(1.7538\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 93600.2.a.f

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