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Properties

Label 6350400.bdq
Number of curves $2$
Conductor $6350400$
CM no
Rank $2$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bdq1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 6350400.bdq have rank \(2\).

Complex multiplication

The elliptic curves in class 6350400.bdq do not have complex multiplication.

Modular form 6350400.2.a.bdq

Copy content sage:E.q_eigenform(10)
 
\(q - 4 q^{13} + 6 q^{17} + 2 q^{19} + O(q^{20})\) 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 6350400.bdq

Copy content sage:E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
6350400.bdq1 \([0, 0, 0, -13891500, 12835746000]\) \(23625/8\) \(100389735898841088000000\) \([]\) \(501645312\) \(3.1159\)
6350400.bdq2 \([0, 0, 0, -5659500, -5181358000]\) \(10481625/2\) \(3825245233152000000\) \([]\) \(167215104\) \(2.5666\)