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SageMath
E = EllipticCurve("tk1")
E.isogeny_class()
Elliptic curves in class 369600tk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.tk2 | 369600tk1 | \([0, 1, 0, -13134833, -18266487537]\) | \(7831544736466064/29831377653\) | \(954604084896000000000\) | \([2]\) | \(22855680\) | \(2.8845\) | \(\Gamma_0(N)\)-optimal |
| 369600.tk1 | 369600tk2 | \([0, 1, 0, -209964833, -1171099797537]\) | \(7997484869919944276/116700507\) | \(14937664896000000000\) | \([2]\) | \(45711360\) | \(3.2310\) |
Rank
sage: E.rank()
The elliptic curves in class 369600tk have rank \(1\).
Complex multiplication
The elliptic curves in class 369600tk do not have complex multiplication.Modular form 369600.2.a.tk
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.
