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SageMath
E = EllipticCurve("fo1")
E.isogeny_class()
Elliptic curves in class 47040fo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
47040.bx2 | 47040fo1 | \([0, -1, 0, -122565, 16110837]\) | \(4927700992/151875\) | \(6275792960640000\) | \([2]\) | \(430080\) | \(1.8069\) | \(\Gamma_0(N)\)-optimal |
47040.bx1 | 47040fo2 | \([0, -1, 0, -294065, -38734863]\) | \(4253563312/1476225\) | \(976011321238732800\) | \([2]\) | \(860160\) | \(2.1535\) |
Rank
sage: E.rank()
The elliptic curves in class 47040fo have rank \(0\).
Complex multiplication
The elliptic curves in class 47040fo do not have complex multiplication.Modular form 47040.2.a.fo
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.