Properties

Label 242760.g
Number of curves $2$
Conductor $242760$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 242760.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
242760.g1 242760g2 \([0, -1, 0, -81016, 8189500]\) \(2379293284/212415\) \(5250234080394240\) \([2]\) \(1474560\) \(1.7563\)  
242760.g2 242760g1 \([0, -1, 0, 5684, 594580]\) \(3286064/26775\) \(-165448552953600\) \([2]\) \(737280\) \(1.4097\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 242760.g have rank \(1\).

Complex multiplication

The elliptic curves in class 242760.g do not have complex multiplication.

Modular form 242760.2.a.g

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.