Properties

Label 257600.fh
Number of curves $4$
Conductor $257600$
CM no
Rank $0$
Graph

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

Elliptic curves in class 257600.fh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
257600.fh1 257600fh4 \([0, -1, 0, -266929633, 1678668331137]\) \(513516182162686336369/1944885031250\) \(7966249088000000000000\) \([2]\) \(69009408\) \(3.4171\)  
257600.fh2 257600fh3 \([0, -1, 0, -16929633, 25418331137]\) \(131010595463836369/7704101562500\) \(31556000000000000000000\) \([2]\) \(34504704\) \(3.0705\)  
257600.fh3 257600fh2 \([0, -1, 0, -4545633, 401019137]\) \(2535986675931409/1450751712200\) \(5942279013171200000000\) \([2]\) \(23003136\) \(2.8678\)  
257600.fh4 257600fh1 \([0, -1, 0, -2945633, -1936580863]\) \(690080604747409/3406760000\) \(13954088960000000000\) \([2]\) \(11501568\) \(2.5212\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 257600.fh have rank \(0\).

Complex multiplication

The elliptic curves in class 257600.fh do not have complex multiplication.

Modular form 257600.2.a.fh

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} + q^{7} + q^{9} - 6 q^{11} - 4 q^{13} - 6 q^{17} + 8 q^{19} + O(q^{20})\) Copy content 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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.