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Properties

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

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bar1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

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

Complex multiplication

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

Modular form 705600.2.a.bar

Copy content sage:E.q_eigenform(10)
 
\(q - q^{13} - 3 q^{17} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 705600.bar

Copy content sage:E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
705600.bar1 \([0, 0, 0, -4483500, -3659810000]\) \(-30642435/56\) \(-18215453491200000000\) \([]\) \(13271040\) \(2.5873\)
705600.bar2 \([0, 0, 0, 7276500, -17873730000]\) \(179685/686\) \(-162668553539788800000000\) \([]\) \(39813120\) \(3.1366\)