Properties

Label 366912ch
Number of curves $3$
Conductor $366912$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("ch1")
 
E.isogeny_class()
 

Elliptic curves in class 366912ch

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
366912.ch3 366912ch1 \([0, 0, 0, 380436, 858833584]\) \(270840023/14329224\) \(-322165003890223742976\) \([]\) \(15925248\) \(2.6148\) \(\Gamma_0(N)\)-optimal
366912.ch2 366912ch2 \([0, 0, 0, -3429804, -23412395216]\) \(-198461344537/10417365504\) \(-234214399755495665565696\) \([]\) \(47775744\) \(3.1641\)  
366912.ch1 366912ch3 \([0, 0, 0, -735419244, -7676400516176]\) \(-1956469094246217097/36641439744\) \(-823812202089182140563456\) \([]\) \(143327232\) \(3.7134\)  

Rank

sage: E.rank()
 

The elliptic curves in class 366912ch have rank \(2\).

Complex multiplication

The elliptic curves in class 366912ch do not have complex multiplication.

Modular form 366912.2.a.ch

sage: E.q_eigenform(10)
 
\(q - 3 q^{5} + 3 q^{11} + q^{13} - 3 q^{17} - 7 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.