Properties

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

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Show commands: SageMath
E = EllipticCurve("do1")
 
E.isogeny_class()
 

Elliptic curves in class 44100do

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
44100.m2 44100do1 \([0, 0, 0, 73500, -18221875]\) \(16384/63\) \(-168852050718750000\) \([2]\) \(368640\) \(1.9884\) \(\Gamma_0(N)\)-optimal
44100.m1 44100do2 \([0, 0, 0, -753375, -220806250]\) \(1102736/147\) \(6303809893500000000\) \([2]\) \(737280\) \(2.3350\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 44100.2.a.do

sage: E.q_eigenform(10)
 
\(q - 4 q^{11} + 2 q^{13} - 2 q^{17} + 2 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.