Properties

Label 54096b
Number of curves $2$
Conductor $54096$
CM no
Rank $0$
Graph

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

Elliptic curves in class 54096b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54096.z2 54096b1 \([0, -1, 0, -76848, -15279984]\) \(-416618810500/598934007\) \(-72155122677292032\) \([2]\) \(516096\) \(1.9269\) \(\Gamma_0(N)\)-optimal
54096.z1 54096b2 \([0, -1, 0, -1505688, -710267760]\) \(1566789944863250/925924041\) \(223096908799199232\) \([2]\) \(1032192\) \(2.2735\)  

Rank

sage: E.rank()
 

The elliptic curves in class 54096b have rank \(0\).

Complex multiplication

The elliptic curves in class 54096b do not have complex multiplication.

Modular form 54096.2.a.b

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