Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("fa1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 93600fa

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
93600.i2 93600fa1 \([0, 0, 0, -1785, -29000]\) \(107850176/117\) \(682344000\) \([2]\) \(57344\) \(0.61068\) \(\Gamma_0(N)\)-optimal
93600.i1 93600fa2 \([0, 0, 0, -2235, -13250]\) \(26463592/13689\) \(638673984000\) \([2]\) \(114688\) \(0.95725\)  

Rank

sage: E.rank()
 

The elliptic curves in class 93600fa have rank \(2\).

Complex multiplication

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

Modular form 93600.2.a.fa

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.