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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 110400bn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
110400.g2 | 110400bn1 | \([0, -1, 0, -1033, 36937]\) | \(-1906624/7935\) | \(-507840000000\) | \([2]\) | \(159744\) | \(0.93129\) | \(\Gamma_0(N)\)-optimal |
110400.g1 | 110400bn2 | \([0, -1, 0, -24033, 1439937]\) | \(2998442888/5175\) | \(2649600000000\) | \([2]\) | \(319488\) | \(1.2779\) |
Rank
sage: E.rank()
The elliptic curves in class 110400bn have rank \(2\).
Complex multiplication
The elliptic curves in class 110400bn do not have complex multiplication.Modular form 110400.2.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.