Properties

Label 384.e
Number of curves $2$
Conductor $384$
CM no
Rank $1$
Graph

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

Elliptic curves in class 384.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
384.e1 384h1 \([0, 1, 0, -35, 69]\) \(19056256/27\) \(6912\) \([2]\) \(48\) \(-0.36010\) \(\Gamma_0(N)\)-optimal
384.e2 384h2 \([0, 1, 0, -25, 119]\) \(-219488/729\) \(-5971968\) \([2]\) \(96\) \(-0.013528\)  

Rank

sage: E.rank()
 

The elliptic curves in class 384.e have rank \(1\).

Complex multiplication

The elliptic curves in class 384.e do not have complex multiplication.

Modular form 384.2.a.e

sage: E.q_eigenform(10)
 
\(q + q^{3} - 4q^{5} - 2q^{7} + q^{9} - 4q^{11} + 2q^{13} - 4q^{15} - 2q^{17} - 8q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.