Properties

Label 1100d
Number of curves $2$
Conductor $1100$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 1100d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1100.d2 1100d1 \([0, 0, 0, -500, 3125]\) \(442368/121\) \(3781250000\) \([2]\) \(480\) \(0.54549\) \(\Gamma_0(N)\)-optimal
1100.d1 1100d2 \([0, 0, 0, -7375, 243750]\) \(88723728/11\) \(5500000000\) \([2]\) \(960\) \(0.89206\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1100d have rank \(1\).

Complex multiplication

The elliptic curves in class 1100d do not have complex multiplication.

Modular form 1100.2.a.d

sage: E.q_eigenform(10)
 
\(q + 2 q^{7} - 3 q^{9} - q^{11} - 6 q^{13} - 2 q^{17} - 4 q^{19} + O(q^{20})\) 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.