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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 316239f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
316239.f2 | 316239f1 | \([1, 0, 0, 416832, -49003641]\) | \(61629875/43659\) | \(-5673999597713266743\) | \([2]\) | \(6819840\) | \(2.2870\) | \(\Gamma_0(N)\)-optimal |
316239.f1 | 316239f2 | \([1, 0, 0, -1862553, -413249364]\) | \(5498372125/2614689\) | \(339809531463050086053\) | \([2]\) | \(13639680\) | \(2.6336\) |
Rank
sage: E.rank()
The elliptic curves in class 316239f have rank \(0\).
Complex multiplication
The elliptic curves in class 316239f do not have complex multiplication.Modular form 316239.2.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.