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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 3366.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3366.m1 | 3366o3 | \([1, -1, 1, -4355456, -3497469033]\) | \(12534210458299016895673/315581882565708\) | \(230059192390401132\) | \([2]\) | \(122880\) | \(2.4396\) | |
3366.m2 | 3366o2 | \([1, -1, 1, -282596, -50200329]\) | \(3423676911662954233/483711578981136\) | \(352625741077248144\) | \([2, 2]\) | \(61440\) | \(2.0930\) | |
3366.m3 | 3366o1 | \([1, -1, 1, -74516, 7063287]\) | \(62768149033310713/6915442583808\) | \(5041357643596032\) | \([4]\) | \(30720\) | \(1.7464\) | \(\Gamma_0(N)\)-optimal |
3366.m4 | 3366o4 | \([1, -1, 1, 460984, -270300009]\) | \(14861225463775641287/51859390496937804\) | \(-37805495672267659116\) | \([2]\) | \(122880\) | \(2.4396\) |
Rank
sage: E.rank()
The elliptic curves in class 3366.m have rank \(0\).
Complex multiplication
The elliptic curves in class 3366.m do not have complex multiplication.Modular form 3366.2.a.m
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.