Properties

Label 425880.bb
Number of curves $2$
Conductor $425880$
CM no
Rank $1$
Graph

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

Elliptic curves in class 425880.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
425880.bb1 425880bb1 \([0, 0, 0, -29897283, 29621302958]\) \(820221748268836/369468094905\) \(1331265079127577229009920\) \([2]\) \(50577408\) \(3.3243\) \(\Gamma_0(N)\)-optimal
425880.bb2 425880bb2 \([0, 0, 0, 103768197, 221805530102]\) \(17147425715207422/12872524043925\) \(-92764392791825579421542400\) \([2]\) \(101154816\) \(3.6709\)  

Rank

sage: E.rank()
 

The elliptic curves in class 425880.bb have rank \(1\).

Complex multiplication

The elliptic curves in class 425880.bb do not have complex multiplication.

Modular form 425880.2.a.bb

sage: E.q_eigenform(10)
 
\(q - q^{5} - q^{7} + 2 q^{11} + 2 q^{17} + 6 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.