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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 768.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
768.g1 | 768c1 | \([0, 1, 0, -23, -51]\) | \(2744000/9\) | \(4608\) | \([2]\) | \(64\) | \(-0.43171\) | \(\Gamma_0(N)\)-optimal |
768.g2 | 768c2 | \([0, 1, 0, -13, -85]\) | \(-8000/81\) | \(-2654208\) | \([2]\) | \(128\) | \(-0.085141\) |
Rank
sage: E.rank()
The elliptic curves in class 768.g have rank \(0\).
Complex multiplication
The elliptic curves in class 768.g do not have complex multiplication.Modular form 768.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.