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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 297024.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
297024.m1 | 297024m4 | \([0, -1, 0, -210049, -36983135]\) | \(15638954062612612/205211097\) | \(13448714452992\) | \([2]\) | \(1572864\) | \(1.6633\) | |
297024.m2 | 297024m3 | \([0, -1, 0, -50209, 3755329]\) | \(213597982529572/31475907099\) | \(2062805047640064\) | \([2]\) | \(1572864\) | \(1.6633\) | |
297024.m3 | 297024m2 | \([0, -1, 0, -13489, -540911]\) | \(16568196345808/1744649361\) | \(28584335130624\) | \([2, 2]\) | \(786432\) | \(1.3168\) | |
297024.m4 | 297024m1 | \([0, -1, 0, 1091, -42275]\) | \(140119918592/822139227\) | \(-841870568448\) | \([2]\) | \(393216\) | \(0.97018\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 297024.m have rank \(2\).
Complex multiplication
The elliptic curves in class 297024.m do not have complex multiplication.Modular form 297024.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.