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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 286110f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
286110.f2 | 286110f1 | \([1, -1, 0, -215070, 46933460]\) | \(-2315685267/658240\) | \(-312729673017516480\) | \([2]\) | \(3981312\) | \(2.0722\) | \(\Gamma_0(N)\)-optimal |
286110.f1 | 286110f2 | \([1, -1, 0, -3648390, 2683036556]\) | \(11304275372307/635800\) | \(302068434164646600\) | \([2]\) | \(7962624\) | \(2.4188\) |
Rank
sage: E.rank()
The elliptic curves in class 286110f have rank \(1\).
Complex multiplication
The elliptic curves in class 286110f do not have complex multiplication.Modular form 286110.2.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.