Properties

Label 92400.do
Number of curves $2$
Conductor $92400$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("do1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 92400.do

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.do1 92400u1 \([0, -1, 0, -3008, -61488]\) \(188183524/3465\) \(55440000000\) \([2]\) \(110592\) \(0.85617\) \(\Gamma_0(N)\)-optimal
92400.do2 92400u2 \([0, -1, 0, -8, -181488]\) \(-2/444675\) \(-14229600000000\) \([2]\) \(221184\) \(1.2027\)  

Rank

sage: E.rank()
 

The elliptic curves in class 92400.do have rank \(1\).

Complex multiplication

The elliptic curves in class 92400.do do not have complex multiplication.

Modular form 92400.2.a.do

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{7} + q^{9} + q^{11} - 8 q^{17} - 8 q^{19} + O(q^{20})\)  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.