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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 203390.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
203390.g1 | 203390k1 | \([1, 1, 0, -1887, -87011]\) | \(-117649/440\) | \(-2781399741560\) | \([]\) | \(314496\) | \(1.0735\) | \(\Gamma_0(N)\)-optimal |
203390.g2 | 203390k2 | \([1, 1, 0, 16603, 2054131]\) | \(80062991/332750\) | \(-2103433554554750\) | \([]\) | \(943488\) | \(1.6228\) |
Rank
sage: E.rank()
The elliptic curves in class 203390.g have rank \(1\).
Complex multiplication
The elliptic curves in class 203390.g do not have complex multiplication.Modular form 203390.2.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.