Properties

Label 44100.d
Number of curves $2$
Conductor $44100$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 44100.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
44100.d1 44100co1 \([0, 0, 0, -10984575, 14021239750]\) \(-177953104/125\) \(-102962228260500000000\) \([]\) \(2177280\) \(2.7764\) \(\Gamma_0(N)\)-optimal
44100.d2 44100co2 \([0, 0, 0, 10624425, 59551402750]\) \(161017136/1953125\) \(-1608784816570312500000000\) \([]\) \(6531840\) \(3.3257\)  

Rank

sage: E.rank()
 

The elliptic curves in class 44100.d have rank \(0\).

Complex multiplication

The elliptic curves in class 44100.d do not have complex multiplication.

Modular form 44100.2.a.d

sage: E.q_eigenform(10)
 
\(q - 6 q^{11} + 2 q^{13} + 6 q^{17} - 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.