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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 60840bn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
60840.h1 | 60840bn1 | \([0, 0, 0, -858, 8957]\) | \(2725888/225\) | \(5765806800\) | \([2]\) | \(30720\) | \(0.61527\) | \(\Gamma_0(N)\)-optimal |
60840.h2 | 60840bn2 | \([0, 0, 0, 897, 40898]\) | \(194672/1875\) | \(-768774240000\) | \([2]\) | \(61440\) | \(0.96184\) |
Rank
sage: E.rank()
The elliptic curves in class 60840bn have rank \(2\).
Complex multiplication
The elliptic curves in class 60840bn do not have complex multiplication.Modular form 60840.2.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 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.