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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 54390p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54390.t2 | 54390p1 | \([1, 0, 1, 50591, -8087404]\) | \(121721586383879/310858430400\) | \(-36572183478129600\) | \([2]\) | \(516096\) | \(1.8619\) | \(\Gamma_0(N)\)-optimal |
54390.t1 | 54390p2 | \([1, 0, 1, -429609, -90873884]\) | \(74533948968883321/12833853739560\) | \(1509890058605494440\) | \([2]\) | \(1032192\) | \(2.2085\) |
Rank
sage: E.rank()
The elliptic curves in class 54390p have rank \(1\).
Complex multiplication
The elliptic curves in class 54390p do not have complex multiplication.Modular form 54390.2.a.p
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.