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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 16820c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16820.b1 | 16820c1 | \([0, 0, 0, -26912, -756059]\) | \(226492416/105125\) | \(1000492825922000\) | \([2]\) | \(60480\) | \(1.5728\) | \(\Gamma_0(N)\)-optimal |
| 16820.b2 | 16820c2 | \([0, 0, 0, 95033, -5707026]\) | \(623331504/453125\) | \(-68999505236000000\) | \([2]\) | \(120960\) | \(1.9194\) |
Rank
sage: E.rank()
The elliptic curves in class 16820c have rank \(1\).
Complex multiplication
The elliptic curves in class 16820c do not have complex multiplication.Modular form 16820.2.a.c
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.
