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Properties

Label 424830.bb
Number of curves $2$
Conductor $424830$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bb1")
 
E.isogeny_class()
 

Elliptic curves in class 424830.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
424830.bb1 424830bb2 \([1, 1, 0, -1682734261828, 840177500560518352]\) \(37769548376817211811066153/1011738331054080\) \(14115515284550149315676362506240\) \([2]\) \(7219445760\) \(5.4906\) \(\Gamma_0(N)\)-optimal*
424830.bb2 424830bb1 \([1, 1, 0, -105040258628, 13161979018702032]\) \(-9186763300983704416553/47730830553907200\) \(-665928380440037854480917174681600\) \([2]\) \(3609722880\) \(5.1440\) \(\Gamma_0(N)\)-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 424830.bb1.

Rank

sage: E.rank()
 

The elliptic curves in class 424830.bb have rank \(0\).

Complex multiplication

The elliptic curves in class 424830.bb do not have complex multiplication.

Modular form 424830.2.a.bb

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{8} + q^{9} + q^{10} + 6 q^{11} - q^{12} + 4 q^{13} + q^{15} + q^{16} - q^{18} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.