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SageMath
E = EllipticCurve("ed1")
E.isogeny_class()
Elliptic curves in class 206400ed
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 206400.bg2 | 206400ed1 | \([0, -1, 0, -60033, -3780063]\) | \(5841725401/1857600\) | \(7608729600000000\) | \([2]\) | \(1327104\) | \(1.7512\) | \(\Gamma_0(N)\)-optimal |
| 206400.bg1 | 206400ed2 | \([0, -1, 0, -380033, 87419937]\) | \(1481933914201/53916840\) | \(220843376640000000\) | \([2]\) | \(2654208\) | \(2.0977\) |
Rank
sage: E.rank()
The elliptic curves in class 206400ed have rank \(1\).
Complex multiplication
The elliptic curves in class 206400ed do not have complex multiplication.Modular form 206400.2.a.ed
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.
