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SageMath
E = EllipticCurve("ft1")
E.isogeny_class()
Elliptic curves in class 463680ft
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
463680.ft1 | 463680ft1 | \([0, 0, 0, -165547308, 515404103632]\) | \(2625564132023811051529/918925030195200000\) | \(175609307991192580915200000\) | \([2]\) | \(110592000\) | \(3.7373\) | \(\Gamma_0(N)\)-optimal |
463680.ft2 | 463680ft2 | \([0, 0, 0, 495055572, 3602533482448]\) | \(70213095586874240921591/69970703040000000000\) | \(-13371609583756247040000000000\) | \([2]\) | \(221184000\) | \(4.0838\) |
Rank
sage: E.rank()
The elliptic curves in class 463680ft have rank \(0\).
Complex multiplication
The elliptic curves in class 463680ft do not have complex multiplication.Modular form 463680.2.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 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.