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SageMath
E = EllipticCurve("cf1")
E.isogeny_class()
Elliptic curves in class 35280.cf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35280.cf1 | 35280cx2 | \([0, 0, 0, -1406643, 642128242]\) | \(68971442301/400\) | \(1785114442137600\) | \([2]\) | \(344064\) | \(2.1167\) | |
35280.cf2 | 35280cx1 | \([0, 0, 0, -89523, 9647218]\) | \(17779581/1280\) | \(5712366214840320\) | \([2]\) | \(172032\) | \(1.7702\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 35280.cf have rank \(1\).
Complex multiplication
The elliptic curves in class 35280.cf do not have complex multiplication.Modular form 35280.2.a.cf
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 LMFDB 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 LMFDB labels.