Properties

Label 44100dj
Number of curves $2$
Conductor $44100$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("dj1")
 
E.isogeny_class()
 

Elliptic curves in class 44100dj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
44100.s2 44100dj1 \([0, 0, 0, 18375, -2786875]\) \(1280/7\) \(-3752267793750000\) \([]\) \(207360\) \(1.6705\) \(\Gamma_0(N)\)-optimal
44100.s1 44100dj2 \([0, 0, 0, -1084125, -434966875]\) \(-262885120/343\) \(-183861121893750000\) \([]\) \(622080\) \(2.2198\)  

Rank

sage: E.rank()
 

The elliptic curves in class 44100dj have rank \(1\).

Complex multiplication

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

Modular form 44100.2.a.dj

sage: E.q_eigenform(10)
 
\(q - 3 q^{11} + 4 q^{13} - 2 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.