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Properties

Label 490g
Number of curves $2$
Conductor $490$
CM no
Rank $1$
Graph

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

Elliptic curves in class 490g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
490.f2 490g1 \([1, 0, 0, -71, 265]\) \(-115501303/25600\) \(-8780800\) \([2]\) \(160\) \(0.052802\) \(\Gamma_0(N)\)-optimal
490.f1 490g2 \([1, 0, 0, -1191, 15721]\) \(544737993463/20000\) \(6860000\) \([2]\) \(320\) \(0.39938\)  

Rank

sage: E.rank()
 

The elliptic curves in class 490g have rank \(1\).

Complex multiplication

The elliptic curves in class 490g do not have complex multiplication.

Modular form 490.2.a.g

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