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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 360672j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
360672.j2 | 360672j1 | \([0, -1, 0, -5298, -145260]\) | \(10648000/117\) | \(180742116672\) | \([2]\) | \(327680\) | \(0.97472\) | \(\Gamma_0(N)\)-optimal |
360672.j1 | 360672j2 | \([0, -1, 0, -9633, 131313]\) | \(1000000/507\) | \(50125813690368\) | \([2]\) | \(655360\) | \(1.3213\) |
Rank
sage: E.rank()
The elliptic curves in class 360672j have rank \(1\).
Complex multiplication
The elliptic curves in class 360672j do not have complex multiplication.Modular form 360672.2.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.