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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 44616.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
44616.r1 | 44616g1 | \([0, 1, 0, -1408, 5552]\) | \(62500/33\) | \(163107529728\) | \([2]\) | \(37632\) | \(0.84303\) | \(\Gamma_0(N)\)-optimal |
44616.r2 | 44616g2 | \([0, 1, 0, 5352, 48816]\) | \(1714750/1089\) | \(-10765096962048\) | \([2]\) | \(75264\) | \(1.1896\) |
Rank
sage: E.rank()
The elliptic curves in class 44616.r have rank \(0\).
Complex multiplication
The elliptic curves in class 44616.r do not have complex multiplication.Modular form 44616.2.a.r
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.