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SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 388416.cg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388416.cg1 | 388416cg1 | \([0, -1, 0, -2408, 43746]\) | \(1000000/63\) | \(97322678208\) | \([2]\) | \(315392\) | \(0.85949\) | \(\Gamma_0(N)\)-optimal |
| 388416.cg2 | 388416cg2 | \([0, -1, 0, 1927, 179865]\) | \(8000/147\) | \(-14533519945728\) | \([2]\) | \(630784\) | \(1.2061\) |
Rank
sage: E.rank()
The elliptic curves in class 388416.cg have rank \(0\).
Complex multiplication
The elliptic curves in class 388416.cg do not have complex multiplication.Modular form 388416.2.a.cg
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.
