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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 100016e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 100016.b2 | 100016e1 | \([0, 1, 0, -242247, -45976760]\) | \(-98260901558505084928/10035449471299\) | \(-160567191540784\) | \([2]\) | \(584064\) | \(1.7590\) | \(\Gamma_0(N)\)-optimal |
| 100016.b1 | 100016e2 | \([0, 1, 0, -3876052, -2938485540]\) | \(25156640481643577374288/262360721\) | \(67164344576\) | \([2]\) | \(1168128\) | \(2.1056\) |
Rank
sage: E.rank()
The elliptic curves in class 100016e have rank \(0\).
Complex multiplication
The elliptic curves in class 100016e do not have complex multiplication.Modular form 100016.2.a.e
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.
