Properties

Label 44880.cf
Number of curves $2$
Conductor $44880$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cf1")
 
E.isogeny_class()
 

Elliptic curves in class 44880.cf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
44880.cf1 44880cq2 \([0, 1, 0, -11505736, 14961224564]\) \(41125104693338423360329/179205840000000000\) \(734027120640000000000\) \([2]\) \(2396160\) \(2.8568\)  
44880.cf2 44880cq1 \([0, 1, 0, -364616, 464399220]\) \(-1308796492121439049/22000592486400000\) \(-90114426824294400000\) \([2]\) \(1198080\) \(2.5102\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 44880.cf have rank \(1\).

Complex multiplication

The elliptic curves in class 44880.cf do not have complex multiplication.

Modular form 44880.2.a.cf

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + 2 q^{7} + q^{9} + q^{11} - q^{15} + q^{17} + 8 q^{19} + O(q^{20})\) 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.