Properties

Label 93600dq
Number of curves $4$
Conductor $93600$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("dq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 93600dq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
93600.f3 93600dq1 \([0, 0, 0, -48825, -4131000]\) \(17657244864/105625\) \(77000625000000\) \([2, 2]\) \(393216\) \(1.5041\) \(\Gamma_0(N)\)-optimal
93600.f4 93600dq2 \([0, 0, 0, -20700, -8856000]\) \(-21024576/714025\) \(-33313550400000000\) \([2]\) \(786432\) \(1.8507\)  
93600.f2 93600dq3 \([0, 0, 0, -78075, 1397250]\) \(9024895368/5078125\) \(29615625000000000\) \([2]\) \(786432\) \(1.8507\)  
93600.f1 93600dq4 \([0, 0, 0, -780075, -265187250]\) \(9001508089608/325\) \(1895400000000\) \([2]\) \(786432\) \(1.8507\)  

Rank

sage: E.rank()
 

The elliptic curves in class 93600dq have rank \(1\).

Complex multiplication

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

Modular form 93600.2.a.dq

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

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.