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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 321776.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 321776.m1 | 321776m2 | \([0, 1, 0, -75768, -988844]\) | \(2433138625/1387778\) | \(27437217138286592\) | \([2]\) | \(1769472\) | \(1.8440\) | |
| 321776.m2 | 321776m1 | \([0, 1, 0, -48728, 4105492]\) | \(647214625/3332\) | \(65875671400448\) | \([2]\) | \(884736\) | \(1.4974\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 321776.m have rank \(2\).
Complex multiplication
The elliptic curves in class 321776.m do not have complex multiplication.Modular form 321776.2.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.
