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SageMath
E = EllipticCurve("nt1")
E.isogeny_class()
Elliptic curves in class 221760nt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 221760.g2 | 221760nt1 | \([0, 0, 0, -12123, -49572]\) | \(156416571072/89676125\) | \(112966090776000\) | \([2]\) | \(663552\) | \(1.3862\) | \(\Gamma_0(N)\)-optimal |
| 221760.g1 | 221760nt2 | \([0, 0, 0, -126468, 17239392]\) | \(2774689708608/13234375\) | \(1066976064000000\) | \([2]\) | \(1327104\) | \(1.7328\) |
Rank
sage: E.rank()
The elliptic curves in class 221760nt have rank \(1\).
Complex multiplication
The elliptic curves in class 221760nt do not have complex multiplication.Modular form 221760.2.a.nt
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.
