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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 11858c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11858.o2 | 11858c1 | \([1, 0, 1, -462586, 78341932]\) | \(1071912625/360448\) | \(3681146072857673728\) | \([]\) | \(201600\) | \(2.2649\) | \(\Gamma_0(N)\)-optimal |
11858.o1 | 11858c2 | \([1, 0, 1, -33664986, 75179514540]\) | \(413160293352625/42592\) | \(434979174624783712\) | \([]\) | \(604800\) | \(2.8142\) |
Rank
sage: E.rank()
The elliptic curves in class 11858c have rank \(0\).
Complex multiplication
The elliptic curves in class 11858c do not have complex multiplication.Modular form 11858.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.