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Properties

Label 80850bb
Number of curves $2$
Conductor $80850$
CM no
Rank $1$
Graph

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

Elliptic curves in class 80850bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
80850.l1 80850bb1 \([1, 1, 0, -2626709950, -51968428068500]\) \(-43612581618346739773945/147358175518034712\) \(-6772086715437994465659375000\) \([]\) \(74649600\) \(4.2044\) \(\Gamma_0(N)\)-optimal
80850.l2 80850bb2 \([1, 1, 0, 5611445675, -270104943417875]\) \(425206334414152986757655/931885180314516223488\) \(-42826312335477546553570200000000\) \([]\) \(223948800\) \(4.7538\)  

Rank

sage: E.rank()
 

The elliptic curves in class 80850bb have rank \(1\).

Complex multiplication

The elliptic curves in class 80850bb do not have complex multiplication.

Modular form 80850.2.a.bb

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} - q^{11} - q^{12} + q^{13} + q^{16} + 6 q^{17} - q^{18} - 5 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.