Properties

Label 405600h
Number of curves $2$
Conductor $405600$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 405600h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
405600.h1 405600h1 \([0, -1, 0, -90978, -10531548]\) \(2156689088/81\) \(3127772232000\) \([2]\) \(1658880\) \(1.4840\) \(\Gamma_0(N)\)-optimal
405600.h2 405600h2 \([0, -1, 0, -86753, -11558223]\) \(-29218112/6561\) \(-16214371250688000\) \([2]\) \(3317760\) \(1.8306\)  

Rank

sage: E.rank()
 

The elliptic curves in class 405600h have rank \(1\).

Complex multiplication

The elliptic curves in class 405600h do not have complex multiplication.

Modular form 405600.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4q^{7} + q^{9} - 8q^{19} + O(q^{20})\)  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 Cremona 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 Cremona labels.