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Properties

Label 458640.hi
Number of curves $2$
Conductor $458640$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("hi1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 458640.hi have rank \(0\).

Complex multiplication

The elliptic curves in class 458640.hi do not have complex multiplication.

Modular form 458640.2.a.hi

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 458640.hi

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
458640.hi1 458640hi2 \([0, 0, 0, -927953523, 10822165684722]\) \(9316717055063573427/57377784953125\) \(544230978638011793856000000\) \([2]\) \(230031360\) \(3.9684\)  
458640.hi2 458640hi1 \([0, 0, 0, -926577603, 10856024048898]\) \(9275335480470938787/355047875\) \(3367645729657477632000\) \([2]\) \(115015680\) \(3.6219\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 458640.hi1.