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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 79350bx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
79350.y2 | 79350bx1 | \([1, 0, 1, 12206399, 12278428148]\) | \(2173899265153175/1961845235712\) | \(-181514689718150292480000\) | \([]\) | \(11860992\) | \(3.1503\) | \(\Gamma_0(N)\)-optimal |
79350.y1 | 79350bx2 | \([1, 0, 1, -275238976, 1778227833998]\) | \(-24923353462910020825/341398360424448\) | \(-31587006117859735633920000\) | \([]\) | \(35582976\) | \(3.6996\) |
Rank
sage: E.rank()
The elliptic curves in class 79350bx have rank \(0\).
Complex multiplication
The elliptic curves in class 79350bx do not have complex multiplication.Modular form 79350.2.a.bx
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.