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SageMath
E = EllipticCurve("ft1")
E.isogeny_class()
Elliptic curves in class 154800.ft
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
154800.ft1 | 154800em2 | \([0, 0, 0, -4500009675, -116189875095750]\) | \(8000051600110940079507/144453125\) | \(181969335000000000000\) | \([2]\) | \(82575360\) | \(3.8784\) | |
154800.ft2 | 154800em1 | \([0, 0, 0, -281259675, -1815343845750]\) | \(1953326569433829507/262451171875\) | \(330612890625000000000000\) | \([2]\) | \(41287680\) | \(3.5318\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 154800.ft have rank \(0\).
Complex multiplication
The elliptic curves in class 154800.ft do not have complex multiplication.Modular form 154800.2.a.ft
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.