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Properties

Label 466578h
Number of curves $2$
Conductor $466578$
CM no
Rank $1$
Graph

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

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 466578h have rank \(1\).

Complex multiplication

The elliptic curves in class 466578h do not have complex multiplication.

Modular form 466578.2.a.h

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 3 q^{5} - q^{8} + 3 q^{10} - 3 q^{11} - 2 q^{13} + q^{16} - 6 q^{17} + 2 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.

Elliptic curves in class 466578h

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
466578.h1 466578h1 \([1, -1, 0, -49296, 4225528]\) \(-67645179/8\) \(-1566811849176\) \([]\) \(1710720\) \(1.3655\) \(\Gamma_0(N)\)-optimal
466578.h2 466578h2 \([1, -1, 0, 6249, 13005341]\) \(189/512\) \(-73101173635155456\) \([]\) \(5132160\) \(1.9148\)