Properties

Label 100800.jd
Number of curves $2$
Conductor $100800$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("jd1")
 
E.isogeny_class()
 

Elliptic curves in class 100800.jd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100800.jd1 100800bg2 \([0, 0, 0, -78300, 8262000]\) \(10536048/245\) \(1234517760000000\) \([2]\) \(442368\) \(1.6817\)  
100800.jd2 100800bg1 \([0, 0, 0, -10800, -243000]\) \(442368/175\) \(55112400000000\) \([2]\) \(221184\) \(1.3351\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 100800.jd have rank \(0\).

Complex multiplication

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

Modular form 100800.2.a.jd

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.