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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 630.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
630.g1 | 630g1 | \([1, -1, 1, -46118, -3792203]\) | \(551105805571803/1376829440\) | \(27100133867520\) | \([2]\) | \(3360\) | \(1.4549\) | \(\Gamma_0(N)\)-optimal |
630.g2 | 630g2 | \([1, -1, 1, -28838, -6681419]\) | \(-134745327251163/903920796800\) | \(-17791873043414400\) | \([2]\) | \(6720\) | \(1.8015\) |
Rank
sage: E.rank()
The elliptic curves in class 630.g have rank \(0\).
Complex multiplication
The elliptic curves in class 630.g do not have complex multiplication.Modular form 630.2.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.