Properties

Label 124930g
Number of curves $2$
Conductor $124930$
CM no
Rank $0$
Graph

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

Elliptic curves in class 124930g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
124930.g1 124930g1 \([1, 0, 0, -808221, 279562801]\) \(65787589563409/10400000\) \(9230038282400000\) \([2]\) \(2371200\) \(2.0739\) \(\Gamma_0(N)\)-optimal
124930.g2 124930g2 \([1, 0, 0, -731341, 334901025]\) \(-48743122863889/26406250000\) \(-23435644076406250000\) \([2]\) \(4742400\) \(2.4205\)  

Rank

sage: E.rank()
 

The elliptic curves in class 124930g have rank \(0\).

Complex multiplication

The elliptic curves in class 124930g do not have complex multiplication.

Modular form 124930.2.a.g

sage: E.q_eigenform(10)
 
\(q + q^{2} - 2 q^{3} + q^{4} - q^{5} - 2 q^{6} - 4 q^{7} + q^{8} + q^{9} - q^{10} + 2 q^{11} - 2 q^{12} + q^{13} - 4 q^{14} + 2 q^{15} + q^{16} - 2 q^{17} + q^{18} + 6 q^{19} + O(q^{20})\) 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.