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Properties

Label 446160.eh
Number of curves $2$
Conductor $446160$
CM no
Rank $2$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("eh1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 446160.eh have rank \(2\).

Complex multiplication

The elliptic curves in class 446160.eh do not have complex multiplication.

Modular form 446160.2.a.eh

Copy content sage:E.q_eigenform(10)
 
\(q + q^{3} - q^{5} - 5 q^{7} + q^{9} + q^{11} - q^{15} - 6 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 446160.eh

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
446160.eh1 446160eh2 \([0, 1, 0, -3080016, 2079438804]\) \(4668056654282578921/213092214885\) \(147507545356554240\) \([]\) \(12644352\) \(2.3702\) \(\Gamma_0(N)\)-optimal*
446160.eh2 446160eh1 \([0, 1, 0, -58816, -5509516]\) \(32506551525721/2578125\) \(1784640000000\) \([]\) \(1806336\) \(1.3973\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 446160.eh1.