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Properties

Label 6350400.na
Number of curves $2$
Conductor $6350400$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("na1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 6350400.na have rank \(1\).

Complex multiplication

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

Modular form 6350400.2.a.na

Copy content sage:E.q_eigenform(10)
 
\(q - 3 q^{11} - 2 q^{13} - 3 q^{17} - 4 q^{19} + O(q^{20})\) 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.na

Copy content sage:E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
6350400.na1 \([0, 0, 0, -153247500, -738873450000]\) \(-1812792825/25088\) \(-5508353135738880000000000\) \([]\) \(1074954240\) \(3.5537\)
6350400.na2 \([0, 0, 0, 552352500, -3712271850000]\) \(1047929175/941192\) \(-16738594159244267520000000000\) \([]\) \(3224862720\) \(4.1030\)