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SageMath
E = EllipticCurve("ii1")
E.isogeny_class()
Elliptic curves in class 369600.ii
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
369600.ii1 | 369600ii2 | \([0, -1, 0, -448833, -14774463]\) | \(19530306557/11114334\) | \(5690539008000000000\) | \([2]\) | \(5898240\) | \(2.2886\) | |
369600.ii2 | 369600ii1 | \([0, -1, 0, 111167, -1894463]\) | \(296740963/174636\) | \(-89413632000000000\) | \([2]\) | \(2949120\) | \(1.9421\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 369600.ii have rank \(1\).
Complex multiplication
The elliptic curves in class 369600.ii do not have complex multiplication.Modular form 369600.2.a.ii
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 LMFDB 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 LMFDB labels.