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Properties

Label 42483.x
Number of curves $2$
Conductor $42483$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 42483.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
42483.x1 42483m2 \([0, -1, 1, -41372, 3252857]\) \(-13549359104/243\) \(-140456317491\) \([]\) \(172800\) \(1.2658\)  
42483.x2 42483m1 \([0, -1, 1, 278, 825]\) \(4096/3\) \(-1734028611\) \([]\) \(34560\) \(0.46111\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 42483.x have rank \(0\).

Complex multiplication

The elliptic curves in class 42483.x do not have complex multiplication.

Modular form 42483.2.a.x

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} - q^{3} + 2 q^{4} - 3 q^{5} - 2 q^{6} + q^{9} - 6 q^{10} + 5 q^{11} - 2 q^{12} + q^{13} + 3 q^{15} - 4 q^{16} + 2 q^{18} + 5 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.