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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 19950o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19950.b2 | 19950o1 | \([1, 1, 0, -625, -13925]\) | \(-43308090025/103996158\) | \(-64997598750\) | \([]\) | \(24000\) | \(0.76295\) | \(\Gamma_0(N)\)-optimal |
19950.b1 | 19950o2 | \([1, 1, 0, -18200, 1764000]\) | \(-1706927698345/2483133408\) | \(-969973987500000\) | \([]\) | \(120000\) | \(1.5677\) |
Rank
sage: E.rank()
The elliptic curves in class 19950o have rank \(0\).
Complex multiplication
The elliptic curves in class 19950o do not have complex multiplication.Modular form 19950.2.a.o
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.