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Properties

Label 249690.g
Number of curves $2$
Conductor $249690$
CM no
Rank $2$
Graph

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

Elliptic curves in class 249690.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
249690.g1 249690g1 \([1, 1, 0, -413, -2307]\) \(7820164617049/2556825600\) \(2556825600\) \([2]\) \(147456\) \(0.50830\) \(\Gamma_0(N)\)-optimal
249690.g2 249690g2 \([1, 1, 0, 1187, -14147]\) \(184715807453351/199504307520\) \(-199504307520\) \([2]\) \(294912\) \(0.85487\)  

Rank

sage: E.rank()
 

The elliptic curves in class 249690.g have rank \(2\).

Complex multiplication

The elliptic curves in class 249690.g do not have complex multiplication.

Modular form 249690.2.a.g

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