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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 46200.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46200.be1 | 46200ch2 | \([0, -1, 0, -2099648, 1171729692]\) | \(7997484869919944276/116700507\) | \(14937664896000\) | \([2]\) | \(571392\) | \(2.0797\) | |
| 46200.be2 | 46200ch1 | \([0, -1, 0, -131348, 18305892]\) | \(7831544736466064/29831377653\) | \(954604084896000\) | \([2]\) | \(285696\) | \(1.7332\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 46200.be have rank \(0\).
Complex multiplication
The elliptic curves in class 46200.be do not have complex multiplication.Modular form 46200.2.a.be
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 LMFDB 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 LMFDB labels.
