Properties

Label 396.a
Number of curves 2
Conductor 396
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("396.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 396.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
396.a1 396b2 [0, 0, 0, -111, 214] [2] 96  
396.a2 396b1 [0, 0, 0, 24, 25] [2] 48 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 396.a have rank \(1\).

Modular form 396.2.a.a

sage: E.q_eigenform(10)
 
\( q - 2q^{5} - 2q^{7} - q^{11} - 2q^{13} - 4q^{17} - 6q^{19} + O(q^{20}) \)

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.