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Properties

Label 486178.bh
Number of curves $2$
Conductor $486178$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bh1")
 
E.isogeny_class()
 

Elliptic curves in class 486178.bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
486178.bh1 486178bh2 \([1, -1, 0, -56985472924, -5235921987301384]\) \(98191033604529537629349729/10906239337336\) \(2273104360507847280702904\) \([]\) \(1659571200\) \(4.5426\)  
486178.bh2 486178bh1 \([1, -1, 0, -114742084, 435504143696]\) \(801581275315909089/70810888830976\) \(14758573986369604748836864\) \([]\) \(237081600\) \(3.5697\) \(\Gamma_0(N)\)-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 486178.bh1.

Rank

sage: E.rank()
 

The elliptic curves in class 486178.bh have rank \(1\).

Complex multiplication

The elliptic curves in class 486178.bh do not have complex multiplication.

Modular form 486178.2.a.bh

sage: E.q_eigenform(10)
 
\(q - q^{2} + 3 q^{3} + q^{4} + q^{5} - 3 q^{6} - q^{8} + 6 q^{9} - q^{10} + 3 q^{12} + 3 q^{15} + q^{16} - 3 q^{17} - 6 q^{18} - 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.