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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 16731a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16731.e2 | 16731a1 | \([1, -1, 1, 24811, 84087748]\) | \(17779581/32166277\) | \(-3055991935725390519\) | \([2]\) | \(241920\) | \(2.2259\) | \(\Gamma_0(N)\)-optimal |
| 16731.e1 | 16731a2 | \([1, -1, 1, -2735804, 1705120876]\) | \(23835655373139/584043889\) | \(55487721345361016283\) | \([2]\) | \(483840\) | \(2.5725\) |
Rank
sage: E.rank()
The elliptic curves in class 16731a have rank \(1\).
Complex multiplication
The elliptic curves in class 16731a do not have complex multiplication.Modular form 16731.2.a.a
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.
