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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)
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.