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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 50430.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
50430.r1 | 50430q2 | \([1, 1, 1, -1401880071, 20202310100979]\) | \(64143574428979927522369/139586300156250\) | \(663049476357702087656250\) | \([2]\) | \(22579200\) | \(3.8176\) | |
50430.r2 | 50430q1 | \([1, 1, 1, -88598821, 308200413479]\) | \(16192145593815022369/729711914062500\) | \(3466207657696508789062500\) | \([2]\) | \(11289600\) | \(3.4711\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 50430.r have rank \(0\).
Complex multiplication
The elliptic curves in class 50430.r do not have complex multiplication.Modular form 50430.2.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.