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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 270480.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
270480.m1 | 270480m1 | \([0, -1, 0, -243637536, 1463697620736]\) | \(1138419279070642590770503/112678869663744000\) | \(158305698998944530432000\) | \([2]\) | \(46448640\) | \(3.4864\) | \(\Gamma_0(N)\)-optimal |
270480.m2 | 270480m2 | \([0, -1, 0, -225287456, 1693455302400]\) | \(-900079102684529025934663/360857020174848000000\) | \(-506978131640208850944000000\) | \([2]\) | \(92897280\) | \(3.8329\) |
Rank
sage: E.rank()
The elliptic curves in class 270480.m have rank \(1\).
Complex multiplication
The elliptic curves in class 270480.m do not have complex multiplication.Modular form 270480.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.