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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 52371c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
52371.e2 | 52371c1 | \([1, -1, 0, -109602, -203066825]\) | \(-1349232625/164333367\) | \(-17734555099555823727\) | \([2]\) | \(675840\) | \(2.3730\) | \(\Gamma_0(N)\)-optimal |
52371.e1 | 52371c2 | \([1, -1, 0, -5894217, -5463595706]\) | \(209849322390625/1882056627\) | \(203108094000262787787\) | \([2]\) | \(1351680\) | \(2.7195\) |
Rank
sage: E.rank()
The elliptic curves in class 52371c have rank \(0\).
Complex multiplication
The elliptic curves in class 52371c do not have complex multiplication.Modular form 52371.2.a.c
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.