Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 384.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
384.b1 384d1 \([0, -1, 0, -3, 3]\) \(16000/3\) \(768\) \([2]\) \(16\) \(-0.72845\) \(\Gamma_0(N)\)-optimal
384.b2 384d2 \([0, -1, 0, 7, 9]\) \(4000/9\) \(-73728\) \([2]\) \(32\) \(-0.38187\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 384.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{7} + q^{9} - 4 q^{11} - 6 q^{13} + 6 q^{17} + O(q^{20})\) Copy content 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.