Properties

Label 397800.x
Number of curves $2$
Conductor $397800$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 397800.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
397800.x1 397800x1 \([0, 0, 0, -3214875, -2210980250]\) \(315042014258500/1262881737\) \(14730252580368000000\) \([2]\) \(8847360\) \(2.5346\) \(\Gamma_0(N)\)-optimal
397800.x2 397800x2 \([0, 0, 0, -1693875, -4308439250]\) \(-23040414103250/330419182041\) \(-7708018678652448000000\) \([2]\) \(17694720\) \(2.8812\)  

Rank

sage: E.rank()
 

The elliptic curves in class 397800.x have rank \(1\).

Complex multiplication

The elliptic curves in class 397800.x do not have complex multiplication.

Modular form 397800.2.a.x

sage: E.q_eigenform(10)
 
\(q - 2 q^{7} - 4 q^{11} + q^{13} - q^{17} - 4 q^{19} + O(q^{20})\) Copy content 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.