Properties

Label 44880.m
Number of curves $2$
Conductor $44880$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 44880.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
44880.m1 44880bk1 \([0, -1, 0, -29941, -2041859]\) \(-724731558068224/24623341875\) \(-100857208320000\) \([]\) \(124416\) \(1.4608\) \(\Gamma_0(N)\)-optimal
44880.m2 44880bk2 \([0, -1, 0, 141419, -7285475]\) \(76363175346569216/49717529296875\) \(-203643000000000000\) \([]\) \(373248\) \(2.0101\)  

Rank

sage: E.rank()
 

The elliptic curves in class 44880.m have rank \(0\).

Complex multiplication

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

Modular form 44880.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{7} + q^{9} + q^{11} + 2 q^{13} + q^{15} + q^{17} - 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.