Properties

Label 100800.iq
Number of curves $4$
Conductor $100800$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("iq1")
 
E.isogeny_class()
 

Elliptic curves in class 100800.iq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100800.iq1 100800oa4 \([0, 0, 0, -201900, 34918000]\) \(2438569736/21\) \(7838208000000\) \([2]\) \(524288\) \(1.6420\)  
100800.iq2 100800oa2 \([0, 0, 0, -12900, 520000]\) \(5088448/441\) \(20575296000000\) \([2, 2]\) \(262144\) \(1.2954\)  
100800.iq3 100800oa1 \([0, 0, 0, -2775, -47000]\) \(3241792/567\) \(413343000000\) \([2]\) \(131072\) \(0.94882\) \(\Gamma_0(N)\)-optimal
100800.iq4 100800oa3 \([0, 0, 0, 14100, 2410000]\) \(830584/7203\) \(-2688505344000000\) \([2]\) \(524288\) \(1.6420\)  

Rank

sage: E.rank()
 

The elliptic curves in class 100800.iq have rank \(2\).

Complex multiplication

The elliptic curves in class 100800.iq do not have complex multiplication.

Modular form 100800.2.a.iq

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.