Properties

Label 705600.cbu
Number of curves $2$
Conductor $705600$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("cbu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 705600.cbu

sage: E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
705600.cbu1 \([0, 0, 0, -247327500, -1584025450000]\) \(-7620530425/526848\) \(-115675415850516480000000000\) \([]\) \(238878720\) \(3.7520\)
705600.cbu2 \([0, 0, 0, 17272500, -2246650000]\) \(2595575/1512\) \(-331976639877120000000000\) \([]\) \(79626240\) \(3.2027\)

Rank

sage: E.rank()
 

The elliptic curves in class 705600.cbu have rank \(1\).

Complex multiplication

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

Modular form 705600.2.a.cbu

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.