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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 20280w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
20280.w2 | 20280w1 | \([0, 1, 0, -56, 105600]\) | \(-4/975\) | \(-4819086105600\) | \([2]\) | \(32256\) | \(1.1125\) | \(\Gamma_0(N)\)-optimal |
20280.w1 | 20280w2 | \([0, 1, 0, -33856, 2349920]\) | \(434163602/7605\) | \(75177743247360\) | \([2]\) | \(64512\) | \(1.4591\) |
Rank
sage: E.rank()
The elliptic curves in class 20280w have rank \(1\).
Complex multiplication
The elliptic curves in class 20280w do not have complex multiplication.Modular form 20280.2.a.w
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.