Properties

Label 372232.e
Number of curves $2$
Conductor $372232$
CM no
Rank $0$
Graph

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

Elliptic curves in class 372232.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
372232.e1 372232e2 \([0, 1, 0, -141128, 20357920]\) \(12576878500/1127\) \(27855913229312\) \([2]\) \(1658880\) \(1.6199\)  
372232.e2 372232e1 \([0, 1, 0, -8188, 363744]\) \(-9826000/3703\) \(-22881643009792\) \([2]\) \(829440\) \(1.2733\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 372232.e have rank \(0\).

Complex multiplication

The elliptic curves in class 372232.e do not have complex multiplication.

Modular form 372232.2.a.e

sage: E.q_eigenform(10)
 
\(q - 2q^{3} + q^{7} + q^{9} - 4q^{11} + 6q^{13} + O(q^{20})\)  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.