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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 185020.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
185020.m1 | 185020r1 | \([0, -1, 0, -736717121, 7696851571970]\) | \(4646415367355940880384/38478378125\) | \(366205386608100050000\) | \([2]\) | \(39513600\) | \(3.5336\) | \(\Gamma_0(N)\)-optimal |
185020.m2 | 185020r2 | \([0, -1, 0, -736208316, 7708013329016]\) | \(-289799689905740628304/835751962890625\) | \(-127263938073310802500000000\) | \([2]\) | \(79027200\) | \(3.8802\) |
Rank
sage: E.rank()
The elliptic curves in class 185020.m have rank \(2\).
Complex multiplication
The elliptic curves in class 185020.m do not have complex multiplication.Modular form 185020.2.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.