Properties

Label 462.g
Number of curves $4$
Conductor $462$
CM no
Rank $0$
Graph

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

Elliptic curves in class 462.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
462.g1 462f4 \([1, 0, 0, -40247, 3104415]\) \(7209828390823479793/49509306\) \(49509306\) \([2]\) \(768\) \(1.0762\)  
462.g2 462f3 \([1, 0, 0, -3507, 6507]\) \(4770223741048753/2740574865798\) \(2740574865798\) \([2]\) \(768\) \(1.0762\)  
462.g3 462f2 \([1, 0, 0, -2517, 48285]\) \(1763535241378513/4612311396\) \(4612311396\) \([2, 2]\) \(384\) \(0.72966\)  
462.g4 462f1 \([1, 0, 0, -97, 1337]\) \(-100999381393/723148272\) \(-723148272\) \([4]\) \(192\) \(0.38308\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 462.g have rank \(0\).

Complex multiplication

The elliptic curves in class 462.g do not have complex multiplication.

Modular form 462.2.a.g

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

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.