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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 364650.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
364650.g1 | 364650g1 | \([1, 1, 0, -164775, 26515125]\) | \(-31665165722871409/1214021952000\) | \(-18969093000000000\) | \([]\) | \(3359232\) | \(1.8932\) | \(\Gamma_0(N)\)-optimal |
364650.g2 | 364650g2 | \([1, 1, 0, 804225, 85318125]\) | \(3681591091760239631/2330227453125000\) | \(-36409803955078125000\) | \([]\) | \(10077696\) | \(2.4425\) |
Rank
sage: E.rank()
The elliptic curves in class 364650.g have rank \(1\).
Complex multiplication
The elliptic curves in class 364650.g do not have complex multiplication.Modular form 364650.2.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.