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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 20691n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
20691.m1 | 20691n1 | \([0, 0, 1, -29766, 2311614]\) | \(-2258403328/480491\) | \(-620538735892779\) | \([]\) | \(86400\) | \(1.5598\) | \(\Gamma_0(N)\)-optimal |
20691.m2 | 20691n2 | \([0, 0, 1, 209814, -13368897]\) | \(790939860992/517504691\) | \(-668340732233742579\) | \([]\) | \(259200\) | \(2.1091\) |
Rank
sage: E.rank()
The elliptic curves in class 20691n have rank \(1\).
Complex multiplication
The elliptic curves in class 20691n do not have complex multiplication.Modular form 20691.2.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.