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Properties

Label 446400df
Number of curves $2$
Conductor $446400$
CM no
Rank $2$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve([0, 0, 0, -1368300, 974388400]) E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 446400df have rank \(2\).

Complex multiplication

The elliptic curves in class 446400df do not have complex multiplication.

Modular form 446400.2.a.df

Copy content sage:E.q_eigenform(10)
 
\(q - 3 q^{7} - 3 q^{11} - q^{13} - 2 q^{17} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 446400df

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
446400.df2 446400df1 \([0, 0, 0, -1368300, 974388400]\) \(-2372030262025/2061298872\) \(-246200218040401920000\) \([]\) \(11059200\) \(2.6101\) \(\Gamma_0(N)\)-optimal
446400.df1 446400df2 \([0, 0, 0, -20563500, -107949890000]\) \(-12882119799145/59982446592\) \(-4477665645114163200000000\) \([]\) \(55296000\) \(3.4148\)