Properties

Label 116380b
Number of curves $2$
Conductor $116380$
CM no
Rank $1$
Graph

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

Elliptic curves in class 116380b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116380.j2 116380b1 \([0, -1, 0, -2821, -2214]\) \(1048576/605\) \(1432987405520\) \([2]\) \(142560\) \(1.0221\) \(\Gamma_0(N)\)-optimal
116380.j1 116380b2 \([0, -1, 0, -31916, -2178520]\) \(94875856/275\) \(10421726585600\) \([2]\) \(285120\) \(1.3687\)  

Rank

sage: E.rank()
 

The elliptic curves in class 116380b have rank \(1\).

Complex multiplication

The elliptic curves in class 116380b do not have complex multiplication.

Modular form 116380.2.a.b

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} - q^{5} + q^{9} - q^{11} - 2 q^{15} + 4 q^{17} + 4 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.