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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 40362f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
40362.a1 | 40362f1 | \([1, 1, 0, -9030056, 9409380396]\) | \(91753989172452937/9968032637892\) | \(8846665658457290080452\) | \([2]\) | \(3225600\) | \(2.9450\) | \(\Gamma_0(N)\)-optimal |
40362.a2 | 40362f2 | \([1, 1, 0, 11987014, 46739900130]\) | \(214628074889266583/1187360416300086\) | \(-1053786740140018725616566\) | \([2]\) | \(6451200\) | \(3.2916\) |
Rank
sage: E.rank()
The elliptic curves in class 40362f have rank \(1\).
Complex multiplication
The elliptic curves in class 40362f do not have complex multiplication.Modular form 40362.2.a.f
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.