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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 281554f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
281554.f2 | 281554f1 | \([1, 0, 1, -149231, 22077486]\) | \(647214625/3332\) | \(1892140347800612\) | \([2]\) | \(1769472\) | \(1.7773\) | \(\Gamma_0(N)\)-optimal |
281554.f1 | 281554f2 | \([1, 0, 1, -232041, -5183566]\) | \(2433138625/1387778\) | \(788076454858954898\) | \([2]\) | \(3538944\) | \(2.1238\) |
Rank
sage: E.rank()
The elliptic curves in class 281554f have rank \(1\).
Complex multiplication
The elliptic curves in class 281554f do not have complex multiplication.Modular form 281554.2.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.