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SageMath
E = EllipticCurve("mx1")
E.isogeny_class()
Elliptic curves in class 374850.mx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
374850.mx1 | 374850mx2 | \([1, -1, 1, -308930, 8010447]\) | \(2433138625/1387778\) | \(1859755247955281250\) | \([2]\) | \(5308416\) | \(2.1954\) | |
374850.mx2 | 374850mx1 | \([1, -1, 1, -198680, -33884553]\) | \(647214625/3332\) | \(4465198674562500\) | \([2]\) | \(2654208\) | \(1.8488\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 374850.mx have rank \(1\).
Complex multiplication
The elliptic curves in class 374850.mx do not have complex multiplication.Modular form 374850.2.a.mx
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.