Properties

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

Related objects

Downloads

Learn more

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

Elliptic curves in class 44100.dj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
44100.dj1 44100m2 \([0, 0, 0, -959175, -354233250]\) \(10536048/245\) \(2269371561660000000\) \([2]\) \(663552\) \(2.3081\)  
44100.dj2 44100m1 \([0, 0, 0, -132300, 10418625]\) \(442368/175\) \(101311230431250000\) \([2]\) \(331776\) \(1.9615\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 44100.2.a.dj

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.