Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("z1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 93600z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
93600.bf2 93600z1 \([0, 0, 0, -15825, -1271000]\) \(-601211584/609375\) \(-444234375000000\) \([2]\) \(368640\) \(1.5062\) \(\Gamma_0(N)\)-optimal
93600.bf1 93600z2 \([0, 0, 0, -297075, -62302250]\) \(497169541448/190125\) \(1108809000000000\) \([2]\) \(737280\) \(1.8528\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 93600.2.a.z

sage: E.q_eigenform(10)
 
\(q - 2q^{7} - 4q^{11} - q^{13} - 6q^{19} + O(q^{20})\)  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 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.