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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 169065.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 169065.bb1 | 169065bg1 | \([1, -1, 0, -336195, -1344704]\) | \(1173340055458817/678770015625\) | \(2431067076252140625\) | \([2]\) | \(2064384\) | \(2.2174\) | \(\Gamma_0(N)\)-optimal |
| 169065.bb2 | 169065bg2 | \([1, -1, 0, 1344510, -11765075]\) | \(75048384514044943/43446533203125\) | \(-155607104050048828125\) | \([2]\) | \(4128768\) | \(2.5640\) |
Rank
sage: E.rank()
The elliptic curves in class 169065.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 169065.bb do not have complex multiplication.Modular form 169065.2.a.bb
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.
