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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 5200.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5200.v1 | 5200q2 | \([0, 1, 0, -853, 9283]\) | \(671088640/2197\) | \(224972800\) | \([]\) | \(2592\) | \(0.46803\) | |
5200.v2 | 5200q1 | \([0, 1, 0, -53, -157]\) | \(163840/13\) | \(1331200\) | \([]\) | \(864\) | \(-0.081277\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5200.v have rank \(0\).
Complex multiplication
The elliptic curves in class 5200.v do not have complex multiplication.Modular form 5200.2.a.v
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.