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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 9675f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9675.f2 | 9675f1 | \([1, -1, 1, -17578730, 28369142272]\) | \(1953326569433829507/262451171875\) | \(80716037750244140625\) | \([2]\) | \(645120\) | \(2.8387\) | \(\Gamma_0(N)\)-optimal |
9675.f1 | 9675f2 | \([1, -1, 1, -281250605, 1815537111022]\) | \(8000051600110940079507/144453125\) | \(44426107177734375\) | \([2]\) | \(1290240\) | \(3.1853\) |
Rank
sage: E.rank()
The elliptic curves in class 9675f have rank \(0\).
Complex multiplication
The elliptic curves in class 9675f do not have complex multiplication.Modular form 9675.2.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.