Properties

Label 3864a
Number of curves $2$
Conductor $3864$
CM no
Rank $0$
Graph

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

Elliptic curves in class 3864a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3864.b2 3864a1 \([0, -1, 0, -1568, -44100]\) \(-416618810500/598934007\) \(-613308423168\) \([2]\) \(5376\) \(0.95392\) \(\Gamma_0(N)\)-optimal
3864.b1 3864a2 \([0, -1, 0, -30728, -2061972]\) \(1566789944863250/925924041\) \(1896292435968\) \([2]\) \(10752\) \(1.3005\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3864a have rank \(0\).

Complex multiplication

The elliptic curves in class 3864a do not have complex multiplication.

Modular form 3864.2.a.a

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