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Properties

Label 400752.fh
Number of curves $2$
Conductor $400752$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("fh1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 400752.fh have rank \(0\).

Complex multiplication

The elliptic curves in class 400752.fh do not have complex multiplication.

Modular form 400752.2.a.fh

Copy content sage:E.q_eigenform(10)
 
\(q + 2 q^{5} + 2 q^{7} + 2 q^{13} - 2 q^{17} - 2 q^{19} + O(q^{20})\) 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 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 400752.fh

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
400752.fh1 400752fh2 \([0, 0, 0, -4719, -23958]\) \(949104/529\) \(6477620675328\) \([2]\) \(491520\) \(1.1486\)  
400752.fh2 400752fh1 \([0, 0, 0, -2904, 59895]\) \(3538944/23\) \(17602230096\) \([2]\) \(245760\) \(0.80203\) \(\Gamma_0(N)\)-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 400752.fh1.