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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 39984bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
39984.i2 | 39984bh1 | \([0, -1, 0, -212, -804]\) | \(1722448/459\) | \(282127104\) | \([]\) | \(22464\) | \(0.32988\) | \(\Gamma_0(N)\)-optimal |
39984.i1 | 39984bh2 | \([0, -1, 0, -6092, 185004]\) | \(40685771728/14739\) | \(9059414784\) | \([]\) | \(67392\) | \(0.87919\) |
Rank
sage: E.rank()
The elliptic curves in class 39984bh have rank \(0\).
Complex multiplication
The elliptic curves in class 39984bh do not have complex multiplication.Modular form 39984.2.a.bh
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.