Properties

Label 369600.fq
Number of curves $2$
Conductor $369600$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("fq1")
 
E.isogeny_class()
 

Elliptic curves in class 369600.fq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.fq1 369600fq2 \([0, -1, 0, -209964833, 1171099797537]\) \(7997484869919944276/116700507\) \(14937664896000000000\) \([2]\) \(45711360\) \(3.2310\)  
369600.fq2 369600fq1 \([0, -1, 0, -13134833, 18266487537]\) \(7831544736466064/29831377653\) \(954604084896000000000\) \([2]\) \(22855680\) \(2.8845\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 369600.fq have rank \(1\).

Complex multiplication

The elliptic curves in class 369600.fq do not have complex multiplication.

Modular form 369600.2.a.fq

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{7} + q^{9} + q^{11} + 4 q^{13} - 6 q^{17} - 4 q^{19} + O(q^{20})\) Copy content 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.