Properties

Label 187200qd
Number of curves $2$
Conductor $187200$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("qd1")
 
E.isogeny_class()
 

Elliptic curves in class 187200qd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
187200.ks1 187200qd1 \([0, 0, 0, -4200, 105250]\) \(-303464448/1625\) \(-43875000000\) \([]\) \(165888\) \(0.88658\) \(\Gamma_0(N)\)-optimal
187200.ks2 187200qd2 \([0, 0, 0, 10800, 560250]\) \(7077888/10985\) \(-216217755000000\) \([]\) \(497664\) \(1.4359\)  

Rank

sage: E.rank()
 

The elliptic curves in class 187200qd have rank \(0\).

Complex multiplication

The elliptic curves in class 187200qd do not have complex multiplication.

Modular form 187200.2.a.qd

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.