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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 18620q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18620.c1 | 18620q1 | \([0, 1, 0, -45145, -3458400]\) | \(5405726654464/407253125\) | \(766606766450000\) | \([2]\) | \(86400\) | \(1.6013\) | \(\Gamma_0(N)\)-optimal |
| 18620.c2 | 18620q2 | \([0, 1, 0, 43300, -15274652]\) | \(298091207216/3525390625\) | \(-106178222500000000\) | \([2]\) | \(172800\) | \(1.9479\) |
Rank
sage: E.rank()
The elliptic curves in class 18620q have rank \(1\).
Complex multiplication
The elliptic curves in class 18620q do not have complex multiplication.Modular form 18620.2.a.q
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.
