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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 189618.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
189618.m1 | 189618w1 | \([1, 0, 1, -33128, -2322058]\) | \(832972004929/610368\) | \(2946129755712\) | \([2]\) | \(903168\) | \(1.3268\) | \(\Gamma_0(N)\)-optimal |
189618.m2 | 189618w2 | \([1, 0, 1, -26368, -3295498]\) | \(-420021471169/727634952\) | \(-3512154935028168\) | \([2]\) | \(1806336\) | \(1.6734\) |
Rank
sage: E.rank()
The elliptic curves in class 189618.m have rank \(0\).
Complex multiplication
The elliptic curves in class 189618.m do not have complex multiplication.Modular form 189618.2.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.