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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 226512.bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 226512.bn1 | 226512et2 | \([0, 0, 0, -51523131, -116943983926]\) | \(5718957389087906/1075876263891\) | \(2845613534049521269512192\) | \([2]\) | \(36126720\) | \(3.4101\) | |
| 226512.bn2 | 226512et1 | \([0, 0, 0, 6455229, -10692841390]\) | \(22494434350748/50367250791\) | \(-66608835669162407402496\) | \([2]\) | \(18063360\) | \(3.0636\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 226512.bn have rank \(1\).
Complex multiplication
The elliptic curves in class 226512.bn do not have complex multiplication.Modular form 226512.2.a.bn
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.
