Properties

Label 762.g
Number of curves $2$
Conductor $762$
CM no
Rank $0$
Graph

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

Elliptic curves in class 762.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
762.g1 762f2 \([1, 0, 0, -2978, -62802]\) \(-2920834212558625/110612682\) \(-110612682\) \([]\) \(540\) \(0.62940\)  
762.g2 762f1 \([1, 0, 0, -8, -216]\) \(-57066625/19997928\) \(-19997928\) \([3]\) \(180\) \(0.080090\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 762.g have rank \(0\).

Complex multiplication

The elliptic curves in class 762.g do not have complex multiplication.

Modular form 762.2.a.g

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.