Properties

Label 100800ct
Number of curves $2$
Conductor $100800$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ct1")
 
E.isogeny_class()
 

Elliptic curves in class 100800ct

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100800.ig2 100800ct1 \([0, 0, 0, -7020, 97200]\) \(59319/28\) \(18059231232000\) \([2]\) \(221184\) \(1.2379\) \(\Gamma_0(N)\)-optimal
100800.ig1 100800ct2 \([0, 0, 0, -93420, 10983600]\) \(139798359/98\) \(63207309312000\) \([2]\) \(442368\) \(1.5845\)  

Rank

sage: E.rank()
 

The elliptic curves in class 100800ct have rank \(1\).

Complex multiplication

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

Modular form 100800.2.a.ct

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