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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 48510j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
48510.bj1 | 48510j1 | \([1, -1, 0, -9228669, 10791812933]\) | \(37537160298467283/5519360000\) | \(12781100635269120000\) | \([2]\) | \(2064384\) | \(2.6804\) | \(\Gamma_0(N)\)-optimal |
48510.bj2 | 48510j2 | \([1, -1, 0, -8381949, 12851544005]\) | \(-28124139978713043/14526050000000\) | \(-33637759972705350000000\) | \([2]\) | \(4128768\) | \(3.0270\) |
Rank
sage: E.rank()
The elliptic curves in class 48510j have rank \(1\).
Complex multiplication
The elliptic curves in class 48510j do not have complex multiplication.Modular form 48510.2.a.j
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.