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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 58870n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
58870.u2 | 58870n1 | \([1, 1, 1, 84, 173]\) | \(77882951/54880\) | \(-46154080\) | \([]\) | \(21600\) | \(0.15911\) | \(\Gamma_0(N)\)-optimal |
58870.u1 | 58870n2 | \([1, 1, 1, -931, -13631]\) | \(-106122119209/28672000\) | \(-24113152000\) | \([]\) | \(64800\) | \(0.70842\) |
Rank
sage: E.rank()
The elliptic curves in class 58870n have rank \(1\).
Complex multiplication
The elliptic curves in class 58870n do not have complex multiplication.Modular form 58870.2.a.n
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.