Properties

Label 4368.e
Number of curves $2$
Conductor $4368$
CM no
Rank $0$
Graph

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

Elliptic curves in class 4368.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4368.e1 4368n2 \([0, -1, 0, -58791936, 173529697152]\) \(-5486773802537974663600129/2635437714\) \(-10794752876544\) \([]\) \(197568\) \(2.7397\)  
4368.e2 4368n1 \([0, -1, 0, 11424, 5306112]\) \(40251338884511/2997011332224\) \(-12275758416789504\) \([]\) \(28224\) \(1.7667\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4368.e have rank \(0\).

Complex multiplication

The elliptic curves in class 4368.e do not have complex multiplication.

Modular form 4368.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - q^{7} + q^{9} - 5q^{11} - q^{13} + q^{15} - 3q^{17} + q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.