Properties

Label 9016.e
Number of curves $2$
Conductor $9016$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9016.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9016.e1 9016i2 \([0, 1, 0, -23928, -1432544]\) \(12576878500/1127\) \(135772593152\) \([2]\) \(15360\) \(1.1762\)  
9016.e2 9016i1 \([0, 1, 0, -1388, -26048]\) \(-9826000/3703\) \(-111527487232\) \([2]\) \(7680\) \(0.82963\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 9016.e have rank \(1\).

Complex multiplication

The elliptic curves in class 9016.e do not have complex multiplication.

Modular form 9016.2.a.e

sage: E.q_eigenform(10)
 
\(q - 2q^{3} + q^{9} + 4q^{11} - 6q^{13} + O(q^{20})\)  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.