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Properties

Label 214774.b
Number of curves $2$
Conductor $214774$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 214774.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
214774.b1 214774h2 \([1, -1, 0, -436584328, -3511048479960]\) \(62167173500157644301993/7582456\) \(1122475614763384\) \([2]\) \(29196288\) \(3.2219\)  
214774.b2 214774h1 \([1, -1, 0, -27286448, -54855321664]\) \(-15177411906818559273/167619938752\) \(-24813766647277870528\) \([2]\) \(14598144\) \(2.8753\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 214774.b have rank \(0\).

Complex multiplication

The elliptic curves in class 214774.b do not have complex multiplication.

Modular form 214774.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 2 q^{5} - q^{7} - q^{8} - 3 q^{9} + 2 q^{10} - 4 q^{11} - 4 q^{13} + q^{14} + q^{16} + 3 q^{18} + 6 q^{19} + O(q^{20})\) 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.