Properties

Label 100.a
Number of curves $4$
Conductor $100$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 100.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100.a1 100a3 \([0, -1, 0, -1033, -12438]\) \(488095744/125\) \(31250000\) \([2]\) \(36\) \(0.42408\)  
100.a2 100a4 \([0, -1, 0, -908, -15688]\) \(-20720464/15625\) \(-62500000000\) \([2]\) \(72\) \(0.77065\)  
100.a3 100a1 \([0, -1, 0, -33, 62]\) \(16384/5\) \(1250000\) \([2]\) \(12\) \(-0.12523\) \(\Gamma_0(N)\)-optimal
100.a4 100a2 \([0, -1, 0, 92, 312]\) \(21296/25\) \(-100000000\) \([2]\) \(24\) \(0.22134\)  

Rank

sage: E.rank()
 

The elliptic curves in class 100.a have rank \(0\).

Complex multiplication

The elliptic curves in class 100.a do not have complex multiplication.

Modular form 100.2.a.a

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.