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Properties

Label 270802.b
Number of curves $2$
Conductor $270802$
CM no
Rank $1$
Graph

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

Elliptic curves in class 270802.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270802.b1 270802b2 \([1, 0, 1, -11792, -415116]\) \(304821217/51842\) \(30836830607282\) \([2]\) \(1075200\) \(1.3090\)  
270802.b2 270802b1 \([1, 0, 1, -3382, 69300]\) \(7189057/644\) \(383066218724\) \([2]\) \(537600\) \(0.96239\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 270802.b have rank \(1\).

Complex multiplication

The elliptic curves in class 270802.b do not have complex multiplication.

Modular form 270802.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} - 2 q^{3} + q^{4} - 2 q^{5} + 2 q^{6} + q^{7} - q^{8} + q^{9} + 2 q^{10} - 6 q^{11} - 2 q^{12} - 4 q^{13} - q^{14} + 4 q^{15} + q^{16} + 2 q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) 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.