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SageMath
E = EllipticCurve("fe1")
E.isogeny_class()
Elliptic curves in class 243360fe
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
243360.fe2 | 243360fe1 | \([0, 0, 0, -837057, -256934756]\) | \(131096512/18225\) | \(9017065202058388800\) | \([2]\) | \(6709248\) | \(2.3636\) | \(\Gamma_0(N)\)-optimal |
243360.fe1 | 243360fe2 | \([0, 0, 0, -3506412, 2269342816]\) | \(150568768/16875\) | \(534344604566423040000\) | \([2]\) | \(13418496\) | \(2.7102\) |
Rank
sage: E.rank()
The elliptic curves in class 243360fe have rank \(0\).
Complex multiplication
The elliptic curves in class 243360fe do not have complex multiplication.Modular form 243360.2.a.fe
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.