Properties

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

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 44100.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
44100.l1 44100p2 \([0, 0, 0, -106575, 13119750]\) \(10536048/245\) \(3112992540000000\) \([2]\) \(221184\) \(1.7587\)  
44100.l2 44100p1 \([0, 0, 0, -14700, -385875]\) \(442368/175\) \(138972881250000\) \([2]\) \(110592\) \(1.4122\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 44100.2.a.l

sage: E.q_eigenform(10)
 
\(q - 4 q^{11} - 2 q^{17} + 6 q^{19} + O(q^{20})\) 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.