Properties

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

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 44100r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
44100.j1 44100r1 \([0, 0, 0, -1852200, 964301625]\) \(3538944/25\) \(4964250291131250000\) \([2]\) \(774144\) \(2.4200\) \(\Gamma_0(N)\)-optimal
44100.j2 44100r2 \([0, 0, 0, -694575, 2155497750]\) \(-11664/625\) \(-1985700116452500000000\) \([2]\) \(1548288\) \(2.7666\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 44100.2.a.r

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