Properties

Label 3648bi
Number of curves $2$
Conductor $3648$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bi1")
 
E.isogeny_class()
 

Elliptic curves in class 3648bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3648.u1 3648bi1 \([0, 1, 0, -24, -54]\) \(24897088/171\) \(10944\) \([2]\) \(448\) \(-0.39116\) \(\Gamma_0(N)\)-optimal
3648.u2 3648bi2 \([0, 1, 0, -9, -105]\) \(-21952/1083\) \(-4435968\) \([2]\) \(896\) \(-0.044591\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3648bi have rank \(0\).

Complex multiplication

The elliptic curves in class 3648bi do not have complex multiplication.

Modular form 3648.2.a.bi

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{5} - 4 q^{7} + q^{9} - 6 q^{11} + 2 q^{13} - 2 q^{15} + 6 q^{17} + q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.