Properties

Label 11592l
Number of curves $2$
Conductor $11592$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11592l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11592.j2 11592l1 \([0, 0, 0, -255, -2014]\) \(-9826000/3703\) \(-691068672\) \([2]\) \(3840\) \(0.40598\) \(\Gamma_0(N)\)-optimal
11592.j1 11592l2 \([0, 0, 0, -4395, -112138]\) \(12576878500/1127\) \(841300992\) \([2]\) \(7680\) \(0.75255\)  

Rank

sage: E.rank()
 

The elliptic curves in class 11592l have rank \(1\).

Complex multiplication

The elliptic curves in class 11592l do not have complex multiplication.

Modular form 11592.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{7} - 4q^{11} + 6q^{13} + O(q^{20})\)  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 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.