Properties

Label 705600.cbn
Number of curves $2$
Conductor $705600$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("cbn1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 705600.cbn

sage: E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
705600.cbn1 \([0, 0, 0, -9893100, -12672203600]\) \(-7620530425/526848\) \(-7403226614433054720000\) \([]\) \(47775744\) \(2.9473\)
705600.cbn2 \([0, 0, 0, 690900, -17973200]\) \(2595575/1512\) \(-21246504952135680000\) \([]\) \(15925248\) \(2.3980\)

Rank

sage: E.rank()
 

The elliptic curves in class 705600.cbn have rank \(0\).

Complex multiplication

The elliptic curves in class 705600.cbn do not have complex multiplication.

Modular form 705600.2.a.cbn

sage: E.q_eigenform(10)
 
\(q + 6q^{11} - q^{13} + 3q^{17} - 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.