Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 93600.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
93600.d1 93600eq1 \([0, 0, 0, -19425, 1042000]\) \(1111934656/65\) \(47385000000\) \([2]\) \(221184\) \(1.1111\) \(\Gamma_0(N)\)-optimal
93600.d2 93600eq2 \([0, 0, 0, -18300, 1168000]\) \(-14526784/4225\) \(-197121600000000\) \([2]\) \(442368\) \(1.4577\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 93600.2.a.d

sage: E.q_eigenform(10)
 
\(q - 4q^{7} - 6q^{11} + q^{13} - 6q^{17} + 6q^{19} + O(q^{20})\)  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 LMFDB 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 LMFDB labels.