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SageMath
E = EllipticCurve("gc1")
E.isogeny_class()
Elliptic curves in class 302016gc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 302016.gc2 | 302016gc1 | \([0, 1, 0, 15327, -916929]\) | \(857375/1287\) | \(-597688059691008\) | \([2]\) | \(983040\) | \(1.5207\) | \(\Gamma_0(N)\)-optimal |
| 302016.gc1 | 302016gc2 | \([0, 1, 0, -100833, -9303681]\) | \(244140625/61347\) | \(28489797511938048\) | \([2]\) | \(1966080\) | \(1.8673\) |
Rank
sage: E.rank()
The elliptic curves in class 302016gc have rank \(0\).
Complex multiplication
The elliptic curves in class 302016gc do not have complex multiplication.Modular form 302016.2.a.gc
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 Cremona 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 Cremona labels.
